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A Primer on the Dirichlet Space

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Title: A Primer on the Dirichlet Space
Description: The 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.
Authors: Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford
Resource Type: eBook.
Subjects: Functions of complex variables, Dirichlet principle, Holomorphic functions
Categories: MATHEMATICS / Calculus, MATHEMATICS / Mathematical Analysis
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 685267
RelevancyScore: 1057
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1057.36352539063
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  Data: The 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.
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  Data: <searchLink fieldCode="DE" term="%22Functions+of+complex+variables%22">Functions of complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22Dirichlet+principle%22">Dirichlet principle</searchLink><br /><searchLink fieldCode="DE" term="%22Holomorphic+functions%22">Holomorphic functions</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 515.9
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Functions of complex variables
        Type: general
      – SubjectFull: Dirichlet principle
        Type: general
      – SubjectFull: Holomorphic functions
        Type: general
    Titles:
      – TitleFull: A Primer on the Dirichlet Space
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Omar El-Fallah
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            NameFull: Karim Kellay
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            NameFull: Javad Mashreghi
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            NameFull: Thomas Ransford
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            NameFull: Omar El-Fallah
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            NameFull: Karim Kellay
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            NameFull: Javad Mashreghi
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            NameFull: Thomas Ransford
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2014
            – D: 14
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9781107047525
            – Type: isbn-electronic
              Value: 9781107732216
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            – Type: volume
              Value: 00203
          Titles:
            – TitleFull: A Primer on the Dirichlet Space
              Type: main
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