Complex Analysis: A Functional Analytic Approach

Complex Analysis: A Functional Analytic Approach

by Friedrich Haslinger


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Complex Analysis: A Functional Analytic Approach by Friedrich Haslinger

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

Product Details

ISBN-13: 9783110417234
Publisher: De Gruyter
Publication date: 11/23/2017
Series: De Gruyter Textbook Series
Pages: 347
Product dimensions: 6.69(w) x 9.45(h) x (d)
Age Range: 18 Years

About the Author

Friedrich Haslinger, University of Vienna, Austria.

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