A primer on the Dirichlet space

• 作者： El-Fallah, Omar, author.
• 其他作者：
  • Kellay, Karim, author.
  • Mashreghi, Javad, author.
  • Ransford, Thomas, author.
• 其他題名：
  • Cambridge tracts in mathematics ;
• 出版： Cambridge : Cambridge University Press
• 叢書名： Cambridge tracts in mathematics ;203
• 主題： Dirichlet principle. , Hilbert space. , Holomorphic functions. , Functions of complex variables.
• ISBN： 9781107239425 (electronic bk.) 、 9781107047525 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Preface -- Basic notions -- Capacity -- Boundary behavior -- Zero sets -- Multipliers -- Conformal invariance -- Harmonically weighted Dirichlet spaces -- Invariant subspaces -- Cyclicity -- Appendix A. Hardy spaces -- Appendix B. The Hardy-Littlewood maximal function -- Appendix C. Positive definite matrices -- Appendix D. Regularization and the rising-sun lemma.
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• 摘要註: 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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