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

Haslinger, Friedrich

Softcover

ISBN 10: 3110417235 ISBN 13: 9783110417234

Publisher: De Gruyter, 2017

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. ContentsComplex numbers and functionsCauchy's Theorem and Cauchy's formulaAnalytic continuationConstruction and approximation of holomorphic functionsHarmonic functionsSeveral complex variablesBergman spacesThe canonical solution operator to Nuclear Fréchet spaces of holomorphic functionsThe -complexThe twisted -complex and Schrödinger operators

About this title

About the Author

Friedrich Haslinger, University of Vienna, Austria.

Edition details

• Publisher: De Gruyter
• Publication date: 2017
• Language: English
• ISBN 10: 3110417235
• ISBN 13: 9783110417234
• Binding: Perfect Paperback
• Number of pages: 347