LINEAR CHANGE OF VARIABLES AND ON SIMPLIFICATION OF EXPRESSIONS IN THE SPACE OF GENERALIZED FUNCTIONS

Abstract

The rigorous mathematical theory of generalized functions contains the definition of a set of basic functions, the definition of a continuous functional, rules for performing limit transitions, delta-like sequences, etc. Special literature is devoted to these questions, in which one can find formulations and proofs of the corresponding theorems (see, for example, the book by V.S. Vladimirov "Generalized functions in mathematical physics", I.M. Gelfand and G.E.Shilov "Generalized functions and actions on them ", MS Agranovich" Generalized functions and Sobolev spaces ", MA Shubin" Lectures on the equations of mathematical physics "and many others). In this article, we will look at techniques for changing a variable in an argument of a generic function, multiplying by a locally integral function, and simplifying expressions.