A Primer on the Dirichlet Space

Released on by Omar El-Fallah
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  • A Primer on the Dirichlet Space Book Detail

  • Author : Omar El-Fallah
  • Release Date : 2014-01-16
  • Publisher : Cambridge University Press
  • Genre : Mathematics
  • Pages : 227
  • ISBN 13 : 1107729777
  • File Size : 37,37 MB
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A Primer on the Dirichlet Space by Omar El-Fallah PDF Summary

Book 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.

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A Primer on the Dirichlet Space

A Primer on the Dirichlet Space

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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

A Primer on the Dirichlet Space

A Primer on the Dirichlet Space

File Size : 42,42 MB
Total View : 8556 Views
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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