Complex analysis : a functional analytic approach
Author(s)
Bibliographic Information
Complex analysis : a functional analytic approach
（De Gruyter graduate）
De Gruyter, c2018
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Note
Includes bibliographical references (p. [331]-333) and index
Description and Table of Contents
Description
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: Frechet 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.
Contents
Complex numbers and functions
Cauchy's Theorem and Cauchy's formula
Analytic continuation
Construction and approximation of holomorphic functions
Harmonic functions
Several complex variables
Bergman spaces
The canonical solution operator to
Nuclear Frechet spaces of holomorphic functions
The -complex
The twisted -complex and Schroedinger operators
by "Nielsen BookData"