The volume is based on the Sobolev-Schwartz concept of Generalized
Functions. It presents general theory including the Fourier,
Laplace, Mellin, Hilbert, Cauchy-Bochner, Poisson integral
transforms and operational calculus. Traditional material is
supplemented by the theory of Fourier series, abelian theorems,
boundary values of helomorphic functions for one and several
variables. There is detailed study of convolution theory,
convolution algebras and convolution equations in them, homogenous
generalized functions and multiplication of generalized functions
and some trends in these problems. Methods of the theory of
generalized functions are applied to some problems in mathematical
physics, for example: fundamental solutions of partial differential
equations and Cauchy problems. This volume also includes numerous
problems, exercises, examples and figures.
General
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