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Methods of the theory of generalized functions. (English) Zbl 1078.46029
Analytical Methods and Special Functions 6. London: Taylor & Francis (ISBN 0-415-27356-0/hbk). xiv, 311 p. £ 62.00 (2002).
Publisher’s description: This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, Abelian theorems, and boundary values of holomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogeneous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.
MSC:
46GxxMeasures, integration, derivative, holomorphy, involving infinite-dimensional spaces
46-02Research monographs (functional analysis)