On Polyanalytic Functions in Several Complex Variables
Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Vasilevski, Nikolai [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2023 |
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| Übergeordnetes Werk: |
Enthalten in: Complex analysis and operator theory - Cham (ZG) : Springer International Publishing AG, 2007, 17(2023), 6 vom: 14. Juli |
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| Übergeordnetes Werk: |
volume:17 ; year:2023 ; number:6 ; day:14 ; month:07 |
| Links: |
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| DOI / URN: |
10.1007/s11785-023-01386-0 |
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| Katalog-ID: |
SPR052252612 |
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| 100 | 1 | |a Vasilevski, Nikolai |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On Polyanalytic Functions in Several Complex Variables |
| 264 | 1 | |c 2023 | |
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| 520 | |a Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. Further we specify the obtained description to different concrete realizations of the above operators and Hilbert spaces %$\mathcal {H}%$, illustrating a variety of possibilities that may occur in the characterisation of the polyanalytic type spaces in several complex variables. | ||
| 650 | 4 | |a Poly-Bergman |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Poly-Fock |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Poly-Vekua |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Extended Fock space construction |7 (dpeaa)DE-He213 | |
| 773 | 0 | 8 | |i Enthalten in |t Complex analysis and operator theory |d Cham (ZG) : Springer International Publishing AG, 2007 |g 17(2023), 6 vom: 14. Juli |w (DE-627)527571288 |w (DE-600)2276146-9 |x 1661-8262 |7 nnns |
| 773 | 1 | 8 | |g volume:17 |g year:2023 |g number:6 |g day:14 |g month:07 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s11785-023-01386-0 |z kostenfrei |3 Volltext |
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10.1007/s11785-023-01386-0 doi (DE-627)SPR052252612 (SPR)s11785-023-01386-0-e DE-627 ger DE-627 rakwb eng Vasilevski, Nikolai verfasserin aut On Polyanalytic Functions in Several Complex Variables 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. Further we specify the obtained description to different concrete realizations of the above operators and Hilbert spaces %$\mathcal {H}%$, illustrating a variety of possibilities that may occur in the characterisation of the polyanalytic type spaces in several complex variables. Poly-Bergman (dpeaa)DE-He213 Poly-Fock (dpeaa)DE-He213 Poly-Vekua (dpeaa)DE-He213 Extended Fock space construction (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 17(2023), 6 vom: 14. Juli (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:17 year:2023 number:6 day:14 month:07 https://dx.doi.org/10.1007/s11785-023-01386-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2023 6 14 07 |
| spelling |
10.1007/s11785-023-01386-0 doi (DE-627)SPR052252612 (SPR)s11785-023-01386-0-e DE-627 ger DE-627 rakwb eng Vasilevski, Nikolai verfasserin aut On Polyanalytic Functions in Several Complex Variables 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. Further we specify the obtained description to different concrete realizations of the above operators and Hilbert spaces %$\mathcal {H}%$, illustrating a variety of possibilities that may occur in the characterisation of the polyanalytic type spaces in several complex variables. Poly-Bergman (dpeaa)DE-He213 Poly-Fock (dpeaa)DE-He213 Poly-Vekua (dpeaa)DE-He213 Extended Fock space construction (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 17(2023), 6 vom: 14. Juli (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:17 year:2023 number:6 day:14 month:07 https://dx.doi.org/10.1007/s11785-023-01386-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2023 6 14 07 |
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10.1007/s11785-023-01386-0 doi (DE-627)SPR052252612 (SPR)s11785-023-01386-0-e DE-627 ger DE-627 rakwb eng Vasilevski, Nikolai verfasserin aut On Polyanalytic Functions in Several Complex Variables 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. Further we specify the obtained description to different concrete realizations of the above operators and Hilbert spaces %$\mathcal {H}%$, illustrating a variety of possibilities that may occur in the characterisation of the polyanalytic type spaces in several complex variables. Poly-Bergman (dpeaa)DE-He213 Poly-Fock (dpeaa)DE-He213 Poly-Vekua (dpeaa)DE-He213 Extended Fock space construction (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 17(2023), 6 vom: 14. Juli (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:17 year:2023 number:6 day:14 month:07 https://dx.doi.org/10.1007/s11785-023-01386-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2023 6 14 07 |
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10.1007/s11785-023-01386-0 doi (DE-627)SPR052252612 (SPR)s11785-023-01386-0-e DE-627 ger DE-627 rakwb eng Vasilevski, Nikolai verfasserin aut On Polyanalytic Functions in Several Complex Variables 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. Further we specify the obtained description to different concrete realizations of the above operators and Hilbert spaces %$\mathcal {H}%$, illustrating a variety of possibilities that may occur in the characterisation of the polyanalytic type spaces in several complex variables. Poly-Bergman (dpeaa)DE-He213 Poly-Fock (dpeaa)DE-He213 Poly-Vekua (dpeaa)DE-He213 Extended Fock space construction (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 17(2023), 6 vom: 14. Juli (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:17 year:2023 number:6 day:14 month:07 https://dx.doi.org/10.1007/s11785-023-01386-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2023 6 14 07 |
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10.1007/s11785-023-01386-0 doi (DE-627)SPR052252612 (SPR)s11785-023-01386-0-e DE-627 ger DE-627 rakwb eng Vasilevski, Nikolai verfasserin aut On Polyanalytic Functions in Several Complex Variables 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. Further we specify the obtained description to different concrete realizations of the above operators and Hilbert spaces %$\mathcal {H}%$, illustrating a variety of possibilities that may occur in the characterisation of the polyanalytic type spaces in several complex variables. Poly-Bergman (dpeaa)DE-He213 Poly-Fock (dpeaa)DE-He213 Poly-Vekua (dpeaa)DE-He213 Extended Fock space construction (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 17(2023), 6 vom: 14. Juli (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:17 year:2023 number:6 day:14 month:07 https://dx.doi.org/10.1007/s11785-023-01386-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2023 6 14 07 |
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Enthalten in Complex analysis and operator theory 17(2023), 6 vom: 14. Juli volume:17 year:2023 number:6 day:14 month:07 |
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Enthalten in Complex analysis and operator theory 17(2023), 6 vom: 14. Juli volume:17 year:2023 number:6 day:14 month:07 |
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The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. 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Vasilevski, Nikolai |
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Vasilevski, Nikolai misc Poly-Bergman misc Poly-Fock misc Poly-Vekua misc Extended Fock space construction On Polyanalytic Functions in Several Complex Variables |
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On Polyanalytic Functions in Several Complex Variables Poly-Bergman (dpeaa)DE-He213 Poly-Fock (dpeaa)DE-He213 Poly-Vekua (dpeaa)DE-He213 Extended Fock space construction (dpeaa)DE-He213 |
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On Polyanalytic Functions in Several Complex Variables |
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on polyanalytic functions in several complex variables |
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On Polyanalytic Functions in Several Complex Variables |
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Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. Further we specify the obtained description to different concrete realizations of the above operators and Hilbert spaces %$\mathcal {H}%$, illustrating a variety of possibilities that may occur in the characterisation of the polyanalytic type spaces in several complex variables. © The Author(s) 2023 |
| abstractGer |
Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. Further we specify the obtained description to different concrete realizations of the above operators and Hilbert spaces %$\mathcal {H}%$, illustrating a variety of possibilities that may occur in the characterisation of the polyanalytic type spaces in several complex variables. © The Author(s) 2023 |
| abstract_unstemmed |
Abstract We give a characterisation of the polyanalytic type subspaces of the Hilbert spaces %$\mathcal {H}%$, being the weighted %$L_2%$ function spaces on a connected simply connected domains %$D \subset \mathbb {C}^n%$. The typical examples considered in the paper are the unit ball %$\mathbb {B}^n%$ and the whole space %$\mathbb {C}^n%$. Our approach is based on the use of the two tuples of operators a=(a1,a2,…,an)andb=(b1,b2,…,bn),%$\begin{aligned} \mathbf {\mathfrak {a}}= (\mathfrak {a}_1, \ \mathfrak {a}_2, \ \ldots , \ \mathfrak {a}_n) \quad \textrm{and} \quad \mathbf {\mathfrak {b}}= (\mathfrak {b}_1, \ \mathfrak {b}_2, \ \ldots , \ \mathfrak {b}_n), \end{aligned}%$which act invariantly in some linear space and satisfy therein the commutation relations aj,bℓ=δj,ℓI,aj,aℓ=0,bj,bℓ=0,j,ℓ=1,2,...,n.%$\begin{aligned} \left[ \mathfrak {a}_j, \mathfrak {b}_{\ell }\right] = \delta _{j,\ell }I, \quad \left[ \mathfrak {a}_j, \mathfrak {a}_{\ell }\right] = 0, \quad \left[ \mathfrak {b}_j, \mathfrak {b}_{\ell }\right] = 0, \quad j,\ell = 1,2,...,n. \end{aligned}%$We assume further that a common invariant domain of the above operators is a dense linear subspace in a Hilbert space %$\mathcal {H}%$, and impose several additional conditions. The exact formulation is given in the Extended Fock space construction. Further we specify the obtained description to different concrete realizations of the above operators and Hilbert spaces %$\mathcal {H}%$, illustrating a variety of possibilities that may occur in the characterisation of the polyanalytic type spaces in several complex variables. © The Author(s) 2023 |
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On Polyanalytic Functions in Several Complex Variables |
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https://dx.doi.org/10.1007/s11785-023-01386-0 |
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10.1007/s11785-023-01386-0 |
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2024-07-04T02:01:08.858Z |
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| score |
7.3998566 |