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A primer on the Dirichlet Spaces

hal.structure.identifierDépartement de Mathématiques
dc.contributor.authorEL-FALLAH, Omar
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorKELLAY, Karim
hal.structure.identifierDépartement de Mathématiques et de Statistiques
dc.contributor.authorMASHREGHI, Javad
hal.structure.identifierDépartement de Mathématiques et de Statistiques
dc.contributor.authorRANSFORD, Thomas
dc.date.accessioned2024-04-04T02:21:55Z
dc.date.available2024-04-04T02:21:55Z
dc.date.created2014-01-14
dc.date.issued2014-01-14
dc.identifier.isbn9781107239425
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189612
dc.description.abstractEnThe Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.
dc.language.isoen
dc.publisherCambridge University Press
dc.title.enA primer on the Dirichlet Spaces
dc.typeOuvrage
dc.identifier.doi10.1017/CBO9781107239425
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
bordeaux.page230
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00835054
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00835054v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2014-01-14&rft.spage=230&rft.epage=230&rft.au=EL-FALLAH,%20Omar&KELLAY,%20Karim&MASHREGHI,%20Javad&RANSFORD,%20Thomas&rft.isbn=9781107239425&rft.genre=unknown


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