Convolution equations in multidimensional spaces. (Uravneniya svertki v mnogomernykh prostranstvakh). (English) Zbl 0582.47041

Napalkov, V. V.

Moskva: ”Nauka” Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 240 p. R. 2.20 (1982).

The book is dedicated to a modern part of science, the study of convolution equations in a complex as well as in a real space. Approximation results for the solution of homogeneous convolution equations by elementary solutions are given. Basic is the decomposition theorem and the uniqueness theorem for hyperfunctions.
The approximation theorem is proved for convolution equations in tube domains, for systems of homogeneous convolution equations and homogeneous equations of infinite order in real domains. Solvability questions of a non-homogeneous convolution equation of a system of non-homogeneous equations are studied. Completely solved is the factorization problem for the convolution operator. Analytic functions of several complex variables are used widely.
For people working in the domain of function theory. Completely accessible for postgraduate students of the mathematical departments of universities.

MSC:

47Gxx	Integral, integro-differential, and pseudodifferential operators
46F15	Hyperfunctions, analytic functionals
47-02	Research exposition (monographs, survey articles) pertaining to operator theory
32-02	Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
44A35	Convolution as an integral transform
47A68	Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47B38	Linear operators on function spaces (general)

Keywords:

Approximation; convolution equations; elementary solutions; hyperfunctions; approximation theorem; tube domains; homogeneous equations of infinite order; system of non-homogeneous equations; factorization problem for the convolution operator