Complex Analysis

A Functional Analytic Approach

Friedrich Haslinger

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English

De Gruyter
23 November 2017

Complex analysis, complex variables; Functional analysis & transforms

Series: De Gruyter Textbook

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.

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 Fréchet spaces of holomorphic functions The -complex The twisted -complex and Schrödinger operators

By: Friedrich Haslinger
Imprint: De Gruyter
Country of Publication: Germany
Dimensions: Height: 240mm, Width: 170mm,
Weight: 659g
ISBN: 9783110417234
ISBN 10: 3110417235
Series: De Gruyter Textbook
Pages: 347
Publication Date: 23 November 2017
Audience: College/higher education , Primary , Primary
Format: Paperback
Publisher's Status: Active

Friedrich Haslinger, University of Vienna, Austria.

Reviews for Complex Analysis: A Functional Analytic Approach

This is a succinct and fairly demanding book, but it is one that repays serious effort. The first half alone, a well-written and elegant exposition of the single variable theory for mathematically mature readers, is worth the price of admission. In addition, because there are not a lot of recent textbooks that cover the multi-variable theory [...], the second half is novel and adds to the value of this book. Professional analysts, or those who aspire to become professional analysts, will want to own this book. MAA Reviews The book is clearly written, in a pleasant style and an elegant layout. The first part can be used for graduate courses in complex analysis, while the more advanced second part is adequate for postgraduate courses, as an introductive text on applications of operator theory on Hilbert spaces of holomorphic functions to partial differential equations in complex variables. S. Cobzas in: Stud. Univ. Babes-Bolyai Math. 63/2 (2018), 285-286