Function and Operator Theory on Large Bergman spaces
The theory of Bergman spaces has been a central subject of study in complex analysis during the past decades. The book [7] by S. Bergman contains the first systematic treat-ment of the Hilbert space of square integrable analytic functions with respect to Lebesgue area measure on a domain. His approa...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/395175 |
| Acceso en línea: | http://hdl.handle.net/10803/395175 |
| Access Level: | acceso abierto |
| Palabra clave: | Funcions analítiques Funciones analíticas Analytic functions Funcions holomorfes Funciones holomorfas Holomorphic functions Operadors de Toeplitz Operadores de Toeplitz Toeplitz operators Equacions funcionals Ecuaciones funcionales Functional equations Nuclis de Bergman Núcleos de Bergman Bergman kernel functions Ciències Experimentals i Matemàtiques 51 |
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Function and Operator Theory on Large Bergman spacesArroussi, HichamFuncions analítiquesFunciones analíticasAnalytic functionsFuncions holomorfesFunciones holomorfasHolomorphic functionsOperadors de ToeplitzOperadores de ToeplitzToeplitz operatorsEquacions funcionalsEcuaciones funcionalesFunctional equationsNuclis de BergmanNúcleos de BergmanBergman kernel functionsCiències Experimentals i Matemàtiques51The theory of Bergman spaces has been a central subject of study in complex analysis during the past decades. The book [7] by S. Bergman contains the first systematic treat-ment of the Hilbert space of square integrable analytic functions with respect to Lebesgue area measure on a domain. His approach was based on a reproducing kernel that became known as the Bergman kernel function. When attention was later directed to the spaces AP over the unit disk, it was natural to call them Bergman spaces. As counterparts of Hardy spaces, they presented analogous problems. However, although many problems in Hardy spaces were well understood by the 1970s, their counterparts for Bergman spaces were generally viewed as intractable, and only some isolated progress was done. The 1980s saw the emerging of operator theoretic studies related to Bergman spaces with important contributions by several authors. Their achievements on Bergman spaces with standard weights are presented in Zhu's book [77]. The main breakthroughs came in the 1990s, where in a flurry of important advances, problems previously considered intractable began to be solved. First came Hedenmalm's construction of canonical divisors [26], then Seip's description [59] of sampling and interpolating sequences on Bergman spaces, and later on, the study of Aleman, Richter and Sundberg [1] on the invariant subspaces of A2, among others. This attracted other workers to the field and inspired a period of intense research on Bergman spaces and related topics. Nowadays there are rich theories on Bergman spaces that can be found on the textbooks [27] and [22]. Meanwhile, also in the nineties, some isolated problems on Bergman spaces with ex-ponential type weights began to be studied. These spaces are large in the sense that they contain all the Bergman spaces with standard weights, and their study presented new dif-ficulties, as the techniques and ideas that led to success when working on the analogous problems for standard Bergman spaces, failed to work on that context. It is the main goal of this work to do a deep study of the function theoretic properties of such spaces, as well as of some operators acting on them. It turns out that large Bergman spaces are close in spirit to Fock spaces [79], and many times mixing classical techniques from both Bergman and Fock spaces in an appropriate way, can led to some success when studying large Bergman spaces.Universitat de BarcelonaPau, JordiOrtega Cerdà, JoaquimUniversitat de Barcelona. Departament de Matemàtiques i Informàtica201620162016info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersion117 p.application/pdfapplication/pdfhttp://hdl.handle.net/10803/395175TDX (Tesis Doctorals en Xarxa)reponame:TDR. Tesis Doctorales en Redinstname:CBUC, CESCAInglésL'accés als continguts d'aquesta tesi queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:www.tdx.cat:10803/3951752026-06-14T12:46:07Z |
| dc.title.none.fl_str_mv |
Function and Operator Theory on Large Bergman spaces |
| title |
Function and Operator Theory on Large Bergman spaces |
| spellingShingle |
Function and Operator Theory on Large Bergman spaces Arroussi, Hicham Funcions analítiques Funciones analíticas Analytic functions Funcions holomorfes Funciones holomorfas Holomorphic functions Operadors de Toeplitz Operadores de Toeplitz Toeplitz operators Equacions funcionals Ecuaciones funcionales Functional equations Nuclis de Bergman Núcleos de Bergman Bergman kernel functions Ciències Experimentals i Matemàtiques 51 |
| title_short |
Function and Operator Theory on Large Bergman spaces |
| title_full |
Function and Operator Theory on Large Bergman spaces |
| title_fullStr |
Function and Operator Theory on Large Bergman spaces |
| title_full_unstemmed |
Function and Operator Theory on Large Bergman spaces |
| title_sort |
Function and Operator Theory on Large Bergman spaces |
| dc.creator.none.fl_str_mv |
Arroussi, Hicham |
| author |
Arroussi, Hicham |
| author_facet |
Arroussi, Hicham |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Pau, Jordi Ortega Cerdà, Joaquim Universitat de Barcelona. Departament de Matemàtiques i Informàtica |
| dc.subject.none.fl_str_mv |
Funcions analítiques Funciones analíticas Analytic functions Funcions holomorfes Funciones holomorfas Holomorphic functions Operadors de Toeplitz Operadores de Toeplitz Toeplitz operators Equacions funcionals Ecuaciones funcionales Functional equations Nuclis de Bergman Núcleos de Bergman Bergman kernel functions Ciències Experimentals i Matemàtiques 51 |
| topic |
Funcions analítiques Funciones analíticas Analytic functions Funcions holomorfes Funciones holomorfas Holomorphic functions Operadors de Toeplitz Operadores de Toeplitz Toeplitz operators Equacions funcionals Ecuaciones funcionales Functional equations Nuclis de Bergman Núcleos de Bergman Bergman kernel functions Ciències Experimentals i Matemàtiques 51 |
| description |
The theory of Bergman spaces has been a central subject of study in complex analysis during the past decades. The book [7] by S. Bergman contains the first systematic treat-ment of the Hilbert space of square integrable analytic functions with respect to Lebesgue area measure on a domain. His approach was based on a reproducing kernel that became known as the Bergman kernel function. When attention was later directed to the spaces AP over the unit disk, it was natural to call them Bergman spaces. As counterparts of Hardy spaces, they presented analogous problems. However, although many problems in Hardy spaces were well understood by the 1970s, their counterparts for Bergman spaces were generally viewed as intractable, and only some isolated progress was done. The 1980s saw the emerging of operator theoretic studies related to Bergman spaces with important contributions by several authors. Their achievements on Bergman spaces with standard weights are presented in Zhu's book [77]. The main breakthroughs came in the 1990s, where in a flurry of important advances, problems previously considered intractable began to be solved. First came Hedenmalm's construction of canonical divisors [26], then Seip's description [59] of sampling and interpolating sequences on Bergman spaces, and later on, the study of Aleman, Richter and Sundberg [1] on the invariant subspaces of A2, among others. This attracted other workers to the field and inspired a period of intense research on Bergman spaces and related topics. Nowadays there are rich theories on Bergman spaces that can be found on the textbooks [27] and [22]. Meanwhile, also in the nineties, some isolated problems on Bergman spaces with ex-ponential type weights began to be studied. These spaces are large in the sense that they contain all the Bergman spaces with standard weights, and their study presented new dif-ficulties, as the techniques and ideas that led to success when working on the analogous problems for standard Bergman spaces, failed to work on that context. It is the main goal of this work to do a deep study of the function theoretic properties of such spaces, as well as of some operators acting on them. It turns out that large Bergman spaces are close in spirit to Fock spaces [79], and many times mixing classical techniques from both Bergman and Fock spaces in an appropriate way, can led to some success when studying large Bergman spaces. |
| publishDate |
2016 |
| dc.date.none.fl_str_mv |
2016 2016 2016 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/doctoralThesis info:eu-repo/semantics/publishedVersion |
| format |
doctoralThesis |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/10803/395175 |
| url |
http://hdl.handle.net/10803/395175 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.rights.none.fl_str_mv |
http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
http://creativecommons.org/licenses/by/4.0/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
117 p. application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
Universitat de Barcelona |
| publisher.none.fl_str_mv |
Universitat de Barcelona |
| dc.source.none.fl_str_mv |
TDX (Tesis Doctorals en Xarxa) reponame:TDR. Tesis Doctorales en Red instname:CBUC, CESCA |
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CBUC, CESCA |
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TDR. Tesis Doctorales en Red |
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TDR. Tesis Doctorales en Red |
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