Primer on the dirichlet space
Material type:
TextLanguage: English Series: Cambridge tracts in mathematics ; 203Publication details: Cambridge : Cambridge University Press, 2014. Description: xiii, 211p. : illustrations ; 24 cmISBN: 9781107047525Subject(s): Dirichlet principle | Hilbert space | Holomorphic functions | Dirichlet-Raum | Functions of complex variablesDDC classification: 517.982.22 Online resources: Table of Contents | Excerpt | Reviews Summary: 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
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SMS Library | 517.982.22 EL-P (Browse shelf(Opens below)) | Available | 25193 |
Includes bibliographical references (pages 197-203) and indexes.
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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