Complex Analysis: A Functional Analytic Approach - Brossura

Haslinger, Friedrich

Brossura

ISBN 10: 3110417235 ISBN 13: 9783110417234

Casa editrice: De Gruyter, 2017

Riassunto

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

Su questo libro

Informazioni sull'autore

Friedrich Haslinger, University of Vienna, Austria.

Dalla quarta di copertina

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

Dettagli dell'edizione

• Editore: De Gruyter
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 3110417235
• ISBN 13: 9783110417234
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 347
• Contatto del produttore: Walter de Gruyter GmbH; productsafety@degruyterbrill.com; ; Genthiner Straße 13; Berlin; 10785; Germania