Vector-Valued Kernels of Bergman Type

Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinat...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Muir, Jerry R. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	Bergman kernels Bergman spaces Reproducing kernels Holomorphic mappings

Anmerkung:	© Springer International Publishing 2017

Übergeordnetes Werk:	Enthalten in: Complex analysis and operator theory - Cham (ZG) : Springer International Publishing AG, 2007, 12(2017), 8 vom: 21. März, Seite 1791-1816
Übergeordnetes Werk:	volume:12 ; year:2017 ; number:8 ; day:21 ; month:03 ; pages:1791-1816

Links:	Volltext

DOI / URN:	10.1007/s11785-017-0662-8

Katalog-ID:	SPR022420002

Internformat


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520			\|a Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinate function of f, provided those coordinate functions each lie in an appropriate Bergman space. Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. The first set of kernels arises naturally from the scalar-valued Bergman kernels, while the second yields the orthogonal projection onto an isomorphic space of scalar-valued functions in the unweighted case.
650		4	\|a Bergman kernels \|7 (dpeaa)DE-He213
650		4	\|a Bergman spaces \|7 (dpeaa)DE-He213
650		4	\|a Reproducing kernels \|7 (dpeaa)DE-He213
650		4	\|a Holomorphic mappings \|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 12(2017), 8 vom: 21. März, Seite 1791-1816 \|w (DE-627)527571288 \|w (DE-600)2276146-9 \|x 1661-8262 \|7 nnns
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matchkey_str	article:16618262:2017----::etraudenlobr
hierarchy_sort_str	2017
publishDate	2017
allfields	10.1007/s11785-017-0662-8 doi (DE-627)SPR022420002 (SPR)s11785-017-0662-8-e DE-627 ger DE-627 rakwb eng Muir, Jerry R. verfasserin aut Vector-Valued Kernels of Bergman Type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinate function of f, provided those coordinate functions each lie in an appropriate Bergman space. Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. The first set of kernels arises naturally from the scalar-valued Bergman kernels, while the second yields the orthogonal projection onto an isomorphic space of scalar-valued functions in the unweighted case. Bergman kernels (dpeaa)DE-He213 Bergman spaces (dpeaa)DE-He213 Reproducing kernels (dpeaa)DE-He213 Holomorphic mappings (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 12(2017), 8 vom: 21. März, Seite 1791-1816 (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:12 year:2017 number:8 day:21 month:03 pages:1791-1816 https://dx.doi.org/10.1007/s11785-017-0662-8 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 12 2017 8 21 03 1791-1816
spelling	10.1007/s11785-017-0662-8 doi (DE-627)SPR022420002 (SPR)s11785-017-0662-8-e DE-627 ger DE-627 rakwb eng Muir, Jerry R. verfasserin aut Vector-Valued Kernels of Bergman Type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinate function of f, provided those coordinate functions each lie in an appropriate Bergman space. Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. The first set of kernels arises naturally from the scalar-valued Bergman kernels, while the second yields the orthogonal projection onto an isomorphic space of scalar-valued functions in the unweighted case. Bergman kernels (dpeaa)DE-He213 Bergman spaces (dpeaa)DE-He213 Reproducing kernels (dpeaa)DE-He213 Holomorphic mappings (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 12(2017), 8 vom: 21. März, Seite 1791-1816 (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:12 year:2017 number:8 day:21 month:03 pages:1791-1816 https://dx.doi.org/10.1007/s11785-017-0662-8 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 12 2017 8 21 03 1791-1816
allfields_unstemmed	10.1007/s11785-017-0662-8 doi (DE-627)SPR022420002 (SPR)s11785-017-0662-8-e DE-627 ger DE-627 rakwb eng Muir, Jerry R. verfasserin aut Vector-Valued Kernels of Bergman Type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinate function of f, provided those coordinate functions each lie in an appropriate Bergman space. Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. The first set of kernels arises naturally from the scalar-valued Bergman kernels, while the second yields the orthogonal projection onto an isomorphic space of scalar-valued functions in the unweighted case. Bergman kernels (dpeaa)DE-He213 Bergman spaces (dpeaa)DE-He213 Reproducing kernels (dpeaa)DE-He213 Holomorphic mappings (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 12(2017), 8 vom: 21. März, Seite 1791-1816 (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:12 year:2017 number:8 day:21 month:03 pages:1791-1816 https://dx.doi.org/10.1007/s11785-017-0662-8 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 12 2017 8 21 03 1791-1816
allfieldsGer	10.1007/s11785-017-0662-8 doi (DE-627)SPR022420002 (SPR)s11785-017-0662-8-e DE-627 ger DE-627 rakwb eng Muir, Jerry R. verfasserin aut Vector-Valued Kernels of Bergman Type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinate function of f, provided those coordinate functions each lie in an appropriate Bergman space. Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. The first set of kernels arises naturally from the scalar-valued Bergman kernels, while the second yields the orthogonal projection onto an isomorphic space of scalar-valued functions in the unweighted case. Bergman kernels (dpeaa)DE-He213 Bergman spaces (dpeaa)DE-He213 Reproducing kernels (dpeaa)DE-He213 Holomorphic mappings (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 12(2017), 8 vom: 21. März, Seite 1791-1816 (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:12 year:2017 number:8 day:21 month:03 pages:1791-1816 https://dx.doi.org/10.1007/s11785-017-0662-8 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 12 2017 8 21 03 1791-1816
allfieldsSound	10.1007/s11785-017-0662-8 doi (DE-627)SPR022420002 (SPR)s11785-017-0662-8-e DE-627 ger DE-627 rakwb eng Muir, Jerry R. verfasserin aut Vector-Valued Kernels of Bergman Type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinate function of f, provided those coordinate functions each lie in an appropriate Bergman space. Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. The first set of kernels arises naturally from the scalar-valued Bergman kernels, while the second yields the orthogonal projection onto an isomorphic space of scalar-valued functions in the unweighted case. Bergman kernels (dpeaa)DE-He213 Bergman spaces (dpeaa)DE-He213 Reproducing kernels (dpeaa)DE-He213 Holomorphic mappings (dpeaa)DE-He213 Enthalten in Complex analysis and operator theory Cham (ZG) : Springer International Publishing AG, 2007 12(2017), 8 vom: 21. März, Seite 1791-1816 (DE-627)527571288 (DE-600)2276146-9 1661-8262 nnns volume:12 year:2017 number:8 day:21 month:03 pages:1791-1816 https://dx.doi.org/10.1007/s11785-017-0662-8 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 12 2017 8 21 03 1791-1816
language	English
source	Enthalten in Complex analysis and operator theory 12(2017), 8 vom: 21. März, Seite 1791-1816 volume:12 year:2017 number:8 day:21 month:03 pages:1791-1816
sourceStr	Enthalten in Complex analysis and operator theory 12(2017), 8 vom: 21. März, Seite 1791-1816 volume:12 year:2017 number:8 day:21 month:03 pages:1791-1816
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Bergman kernels Bergman spaces Reproducing kernels Holomorphic mappings
isfreeaccess_bool	false
container_title	Complex analysis and operator theory
authorswithroles_txt_mv	Muir, Jerry R. @@aut@@
publishDateDaySort_date	2017-03-21T00:00:00Z
hierarchy_top_id	527571288
id	SPR022420002
language_de	englisch
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Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. 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author	Muir, Jerry R.
spellingShingle	Muir, Jerry R. misc Bergman kernels misc Bergman spaces misc Reproducing kernels misc Holomorphic mappings Vector-Valued Kernels of Bergman Type
authorStr	Muir, Jerry R.
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topic_title	Vector-Valued Kernels of Bergman Type Bergman kernels (dpeaa)DE-He213 Bergman spaces (dpeaa)DE-He213 Reproducing kernels (dpeaa)DE-He213 Holomorphic mappings (dpeaa)DE-He213
topic	misc Bergman kernels misc Bergman spaces misc Reproducing kernels misc Holomorphic mappings
topic_unstemmed	misc Bergman kernels misc Bergman spaces misc Reproducing kernels misc Holomorphic mappings
topic_browse	misc Bergman kernels misc Bergman spaces misc Reproducing kernels misc Holomorphic mappings
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title	Vector-Valued Kernels of Bergman Type
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title_full	Vector-Valued Kernels of Bergman Type
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doi_str_mv	10.1007/s11785-017-0662-8
title_sort	vector-valued kernels of bergman type
title_auth	Vector-Valued Kernels of Bergman Type
abstract	Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinate function of f, provided those coordinate functions each lie in an appropriate Bergman space. Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. The first set of kernels arises naturally from the scalar-valued Bergman kernels, while the second yields the orthogonal projection onto an isomorphic space of scalar-valued functions in the unweighted case. © Springer International Publishing 2017
abstractGer	Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinate function of f, provided those coordinate functions each lie in an appropriate Bergman space. Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. The first set of kernels arises naturally from the scalar-valued Bergman kernels, while the second yields the orthogonal projection onto an isomorphic space of scalar-valued functions in the unweighted case. © Springer International Publishing 2017
abstract_unstemmed	Abstract Bergman reproducing integral formulas can be obtained for holomorphic mappings %$f{:}\,{\mathbb {B}}\rightarrow {\mathbb {C}}^n,\,{\mathbb {B}}%$ the open unit ball of %${\mathbb {C}}^n%$, by applying the well-known formulas for scalar-valued functions on %${\mathbb {B}}%$ to each coordinate function of f, provided those coordinate functions each lie in an appropriate Bergman space. Here, we consider an alternative formulation whereby f is reproduced as the integral of the product of a fixed vector-valued kernel and the scalar expression %$\langle f(z),z \rangle ,\,z\in {\mathbb {B}}%$, where %$\langle \cdot ,\cdot \rangle %$ is the Hermitian inner product in %${\mathbb {C}}^n%$. We provide two different classes of vector-valued kernels that reproduce holomorphic mappings lying in spaces properly containing the weighted vector-valued Bergman spaces. An analysis of these larger spaces is given. The first set of kernels arises naturally from the scalar-valued Bergman kernels, while the second yields the orthogonal projection onto an isomorphic space of scalar-valued functions in the unweighted case. © Springer International Publishing 2017
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container_issue	8
title_short	Vector-Valued Kernels of Bergman Type
url	https://dx.doi.org/10.1007/s11785-017-0662-8
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doi_str	10.1007/s11785-017-0662-8
up_date	2024-07-04T02:59:58.108Z
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score	7.400943

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Vector-Valued Kernels of Bergman Type

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