Complex analysis : a functional analytic approach

In this textbook, a concise approach to complex analysis of one and several variables is presented.After an introduction of Cauchy's integral theorem general versions of Runge's approximation theorem and Mittag-Leffler's theorem are discussed.The fi rst part ends with an analytic char...

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Bibliographic Details
Main Author: Haslinger, Friedrich
Format: eBook Book
Language:English
Published: Berlin De Gruyter 2018
Walter de Gruyter GmbH
Edition:1
Series:De Gruyter Textbook
Subjects:
analytic continuation
Bergman kernel
Cauchy integral theorem
Complex analysis
MATHEMATICS / Complex Analysis
MATHEMATICS / Functional Analysis
Mathematics-Textbooks
analytic continuation
Cauchy integral theorem
Complex analysis
Bergman kernel
ISBN:3110417235, 9783110417234
Online Access:Get full text
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Table of Contents:
  • Intro -- Preface -- Contents -- 1. Complex numbers and functions -- 2. Cauchy's Theorem and Cauchy's formula -- 3. Analytic continuation -- 4. Construction and approximation of holomorphic functions -- 5. Harmonic functions -- 6. Several complex variables -- 7. Bergman spaces -- 8. The canonical solution operator to ∂̄ -- 9. Nuclear Fréchet spaces of holomorphic functions -- 10. The ∂̄-complex -- 11. The twisted ∂̄-complex and Schrödinger operators -- Bibliography -- Index
  • 2. Cauchy’s Theorem and Cauchy’s formula --
  • Contents --
  • 9. Nuclear Fréchet spaces of holomorphic functions --
  • Preface --
  • 5. Harmonic functions --
  • 1. Complex numbers and functions --
  • 7. Bergman spaces --
  • Index
  • 6. Several complex variables --
  • 10. The ∂̄-complex --
  • 3. Analytic continuation --
  • Frontmatter --
  • 11. The twisted ∂̄-complex and Schrödinger operators --
  • 4. Construction and approximation of holomorphic functions --
  • Bibliography --
  • 8. The canonical solution operator to ∂̄ --