An Advanced Complex Analysis Problem Book

Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions

  • Daniel Alpay

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Analytic Functions

    1. Front Matter
      Pages 9-9
    2. Daniel Alpay
      Pages 11-60
    3. Daniel Alpay
      Pages 61-118
  3. Topology and Functional Analysis

    1. Front Matter
      Pages 119-119
    2. Daniel Alpay
      Pages 121-198
    3. Daniel Alpay
      Pages 199-247
    4. Daniel Alpay
      Pages 249-283
    5. Daniel Alpay
      Pages 285-327
  4. Hilbert Spaces of Analytic Functions

    1. Front Matter
      Pages 329-329
    2. Daniel Alpay
      Pages 405-441
    3. Daniel Alpay
      Pages 443-459
    4. Daniel Alpay
      Pages 461-474
    5. Daniel Alpay
      Pages 475-486
  5. Back Matter
    Pages 487-521

About this book


This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.


Fourier transform Hilbert spaces of analytic functions complex variable reproducing kernel space topological vector spaces

Authors and affiliations

  • Daniel Alpay
    • 1
  1. 1.Department of MathematicsBen-Gurion University of the Negev Dept of Math, Bldg 37Beer-ShevaIsrael

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-16058-0
  • Online ISBN 978-3-319-16059-7
  • About this book
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