Methods of the Theory of Generalized Functions

Based on the Sobolev-Schwartz concept of Generalized Functions, this text presents general theory including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner, Poisson integraltransforms and operational calculus. The theory of Fourier series, abelian theorems, boundary values of helomorphic functions for one and several variables is covered.
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 helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous 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.