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Complex Analysis: A Functional Analytic Approach (De Gruyter Textbook)

Haslinger, Friedrich

 
9783110417234: Complex Analysis: A Functional Analytic Approach (De Gruyter Textbook)
ISBN 10: 3110417235 ISBN 13: 9783110417234
Verlag: De Gruyter, 2017

Inhaltsangabe

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

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Über die Autorin bzw. den Autor

Friedrich Haslinger, University of Vienna, Austria.

Von der hinteren Coverseite

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

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
De Gruyter
Erscheinungsdatum
2017
Sprache
Englisch
ISBN 10 
3110417235
ISBN 13 
9783110417234
Einband
Broschiert
Auflage
1
Anzahl der Seiten
347
Kontakt zum Hersteller
Walter de Gruyter GmbH
productsafety@degruyterbrill.com

Genthiner Straße 13
Berlin
10785
Deutschland