G. E. Shilov – författare

Generalized Functions, Volume 1: Properties and Operations provides a systematic development of the theory of generalized functions and problems in analysis connected with it. This book focuses on the concept of a convenient link that connects many aspects of analysis, functional analysis, theory of differential equations, representation theory of locally compact Lie groups, and theory of probability and statistics. This volume is essentially devoted to algorithmic questions of the theory, covering many applications of generalized functions to various problems of analysis. The topics discussed include the local properties of generalized functions, differentiation as a continuous operation, and Fourier Transforms of test functions. The wave equation in space of odd dimension, derivation of Green''s theorem, and reducible singular points are also described. This publication is a good reference for mathematicians, researchers, and students concerned with generalized functions.

Spaces of Fundamental and Generalized Functions, Volume 2, analyzes the general theory of linear topological spaces. The basis of the theory of generalized functions is the theory of the so-called countably normed spaces (with compatible norms), their unions (inductive limits), and also of the spaces conjugate to the countably normed ones or their unions. This set of spaces is sufficiently broad on the one hand, and sufficiently convenient for the analyst on the other. The book opens with a chapter that discusses the theory of these spaces. This is followed by separate chapters on fundamental and generalized functions, Fourier transformations of fundamental and generalized functions, and spaces of type S.