Complex Analysis: A Functional Analytic Approach

✍ Scribed by Friedrich Haslinger

• Tongue: English
• Leaves: 349
• Category: Library

✦ Synopsis

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 characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator.

✦ Table of Contents

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