Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators

Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ o...
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Autor*in:	Ivanov, P. A. [verfasserIn] Melikhov, S. N.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Duhamel product backward shift operator space of holomorphic functions

Anmerkung:	© Pleiades Publishing, Ltd. 2023

Übergeordnetes Werk:	Enthalten in: Mathematical notes - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967, 113(2023), 5-6 vom: Juni, Seite 650-662
Übergeordnetes Werk:	volume:113 ; year:2023 ; number:5-6 ; month:06 ; pages:650-662

Links:	Volltext

DOI / URN:	10.1134/S000143462305005X

Katalog-ID:	SPR051960230

Internformat


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520			\|a Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. In the case where, in addition, the domain %$\Omega%$ is convex, it is shown that the operation %$\circledast%$ is realized by means of the adjoint of the Laplace transform as Duhamel product.
650		4	\|a Duhamel product \|7 (dpeaa)DE-He213
650		4	\|a backward shift operator \|7 (dpeaa)DE-He213
650		4	\|a space of holomorphic functions \|7 (dpeaa)DE-He213
700	1		\|a Melikhov, S. N. \|4 aut
773	0	8	\|i Enthalten in \|t Mathematical notes \|d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 \|g 113(2023), 5-6 vom: Juni, Seite 650-662 \|w (DE-627)32557328X \|w (DE-600)2037663-7 \|x 1573-8876 \|7 nnns
773	1	8	\|g volume:113 \|g year:2023 \|g number:5-6 \|g month:06 \|g pages:650-662
856	4	0	\|u https://dx.doi.org/10.1134/S000143462305005X \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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Indexfelder

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allfields	10.1134/S000143462305005X doi (DE-627)SPR051960230 (SPR)S000143462305005X-e DE-627 ger DE-627 rakwb eng Ivanov, P. A. verfasserin aut Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. In the case where, in addition, the domain %$\Omega%$ is convex, it is shown that the operation %$\circledast%$ is realized by means of the adjoint of the Laplace transform as Duhamel product. Duhamel product (dpeaa)DE-He213 backward shift operator (dpeaa)DE-He213 space of holomorphic functions (dpeaa)DE-He213 Melikhov, S. N. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 5-6 vom: Juni, Seite 650-662 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:5-6 month:06 pages:650-662 https://dx.doi.org/10.1134/S000143462305005X lizenzpflichtig 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_206 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 113 2023 5-6 06 650-662
spelling	10.1134/S000143462305005X doi (DE-627)SPR051960230 (SPR)S000143462305005X-e DE-627 ger DE-627 rakwb eng Ivanov, P. A. verfasserin aut Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. In the case where, in addition, the domain %$\Omega%$ is convex, it is shown that the operation %$\circledast%$ is realized by means of the adjoint of the Laplace transform as Duhamel product. Duhamel product (dpeaa)DE-He213 backward shift operator (dpeaa)DE-He213 space of holomorphic functions (dpeaa)DE-He213 Melikhov, S. N. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 5-6 vom: Juni, Seite 650-662 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:5-6 month:06 pages:650-662 https://dx.doi.org/10.1134/S000143462305005X lizenzpflichtig 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_206 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 113 2023 5-6 06 650-662
allfields_unstemmed	10.1134/S000143462305005X doi (DE-627)SPR051960230 (SPR)S000143462305005X-e DE-627 ger DE-627 rakwb eng Ivanov, P. A. verfasserin aut Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. In the case where, in addition, the domain %$\Omega%$ is convex, it is shown that the operation %$\circledast%$ is realized by means of the adjoint of the Laplace transform as Duhamel product. Duhamel product (dpeaa)DE-He213 backward shift operator (dpeaa)DE-He213 space of holomorphic functions (dpeaa)DE-He213 Melikhov, S. N. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 5-6 vom: Juni, Seite 650-662 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:5-6 month:06 pages:650-662 https://dx.doi.org/10.1134/S000143462305005X lizenzpflichtig 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_206 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 113 2023 5-6 06 650-662
allfieldsGer	10.1134/S000143462305005X doi (DE-627)SPR051960230 (SPR)S000143462305005X-e DE-627 ger DE-627 rakwb eng Ivanov, P. A. verfasserin aut Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. In the case where, in addition, the domain %$\Omega%$ is convex, it is shown that the operation %$\circledast%$ is realized by means of the adjoint of the Laplace transform as Duhamel product. Duhamel product (dpeaa)DE-He213 backward shift operator (dpeaa)DE-He213 space of holomorphic functions (dpeaa)DE-He213 Melikhov, S. N. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 5-6 vom: Juni, Seite 650-662 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:5-6 month:06 pages:650-662 https://dx.doi.org/10.1134/S000143462305005X lizenzpflichtig 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_206 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 113 2023 5-6 06 650-662
allfieldsSound	10.1134/S000143462305005X doi (DE-627)SPR051960230 (SPR)S000143462305005X-e DE-627 ger DE-627 rakwb eng Ivanov, P. A. verfasserin aut Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. In the case where, in addition, the domain %$\Omega%$ is convex, it is shown that the operation %$\circledast%$ is realized by means of the adjoint of the Laplace transform as Duhamel product. Duhamel product (dpeaa)DE-He213 backward shift operator (dpeaa)DE-He213 space of holomorphic functions (dpeaa)DE-He213 Melikhov, S. N. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 5-6 vom: Juni, Seite 650-662 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:5-6 month:06 pages:650-662 https://dx.doi.org/10.1134/S000143462305005X lizenzpflichtig 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_206 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 113 2023 5-6 06 650-662
language	English
source	Enthalten in Mathematical notes 113(2023), 5-6 vom: Juni, Seite 650-662 volume:113 year:2023 number:5-6 month:06 pages:650-662
sourceStr	Enthalten in Mathematical notes 113(2023), 5-6 vom: Juni, Seite 650-662 volume:113 year:2023 number:5-6 month:06 pages:650-662
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Duhamel product backward shift operator space of holomorphic functions
isfreeaccess_bool	false
container_title	Mathematical notes
authorswithroles_txt_mv	Ivanov, P. A. @@aut@@ Melikhov, S. N. @@aut@@
publishDateDaySort_date	2023-06-01T00:00:00Z
hierarchy_top_id	32557328X
id	SPR051960230
language_de	englisch
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author	Ivanov, P. A.
spellingShingle	Ivanov, P. A. misc Duhamel product misc backward shift operator misc space of holomorphic functions Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators
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topic_title	Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators Duhamel product (dpeaa)DE-He213 backward shift operator (dpeaa)DE-He213 space of holomorphic functions (dpeaa)DE-He213
topic	misc Duhamel product misc backward shift operator misc space of holomorphic functions
topic_unstemmed	misc Duhamel product misc backward shift operator misc space of holomorphic functions
topic_browse	misc Duhamel product misc backward shift operator misc space of holomorphic functions
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title	Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators
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title_full	Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators
author_sort	Ivanov, P. A.
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author_browse	Ivanov, P. A. Melikhov, S. N.
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author-letter	Ivanov, P. A.
doi_str_mv	10.1134/S000143462305005X
title_sort	many-dimensional duhamel product in the space of holomorphic functions and backward shift operators
title_auth	Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators
abstract	Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. In the case where, in addition, the domain %$\Omega%$ is convex, it is shown that the operation %$\circledast%$ is realized by means of the adjoint of the Laplace transform as Duhamel product. © Pleiades Publishing, Ltd. 2023
abstractGer	Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. In the case where, in addition, the domain %$\Omega%$ is convex, it is shown that the operation %$\circledast%$ is realized by means of the adjoint of the Laplace transform as Duhamel product. © Pleiades Publishing, Ltd. 2023
abstract_unstemmed	Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. In the case where, in addition, the domain %$\Omega%$ is convex, it is shown that the operation %$\circledast%$ is realized by means of the adjoint of the Laplace transform as Duhamel product. © Pleiades Publishing, Ltd. 2023
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title_short	Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators
url	https://dx.doi.org/10.1134/S000143462305005X
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author2	Melikhov, S. N.
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doi_str	10.1134/S000143462305005X
up_date	2024-07-04T00:38:16.985Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR051960230</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230621064750.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230621s2023 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S000143462305005X</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR051960230</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)S000143462305005X-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ivanov, P. A.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Pleiades Publishing, Ltd. 2023</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The system %$\mathcal D_0%$ of partial backward shift operators in a countable inductive limit %$E%$ of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant %$\mathcal K(\mathcal D_0)%$ in the algebra of all continuous linear operators on %$E%$ operators is described. In the topological dual of %$E%$, a multiplication %$\circledast%$ is introduced and studied, which is determined by shifts associated with the system %$\mathcal D_0%$. For a domain %$\Omega%$ in %$\mathbb C^N%$ polystar-shaped with respect to 0, Duhamel product in the space %$H(\Omega)%$ of all holomorphic functions on %$\Omega%$ is studied. 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