A Complex Analysis Problem Book

  • Daniel Alpay

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Complex Numbers

    1. Front Matter
      Pages 9-9
    2. Daniel Alpay
      Pages 11-64
    3. Daniel Alpay
      Pages 65-91
    4. Daniel Alpay
      Pages 93-148
  3. Functions of a Complex Variable

  4. Applications and More Advanced Topics

    1. Front Matter
      Pages 415-415
    2. Daniel Alpay
      Pages 417-442
    3. Daniel Alpay
      Pages 443-456
    4. Daniel Alpay
      Pages 473-490
    5. Daniel Alpay
      Pages 491-509
  5. Appendix

    1. Front Matter
      Pages 511-511
    2. Daniel Alpay
      Pages 513-527
    3. Daniel Alpay
      Pages 529-543

About this book


This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration.

Benefits of the 2nd edition

Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.


analytic function Cauchy formula complex variables conformal mapping holomorphic function positive matrices reproducing kernel

Authors and affiliations

  • Daniel Alpay
    • 1
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer ShevaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42181-0
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-42179-7
  • Online ISBN 978-3-319-42181-0
  • About this book