Asymptotic Functions of Many Variables and Singular Operations with Schwartz Distributions.

摘要

A theory of the asymptotic functions for the case of many variables is presented. It is shown that the class F(R/sup N/) of these generalized functions is closed in respect to the linear algebraic and analytic operations, multiplication as well as a set of linear and polynomial changes of the variables. The existence in F(R/sup N/) of analogues (consistent with the linear operations) of the Schwartz distributions with point support is proved. In terms of these analogues, some formulae for singular products and changes of variables of the Dirac delta-function and its derivatives delta/sup (i)/(x), x is an element of R/sup N/, are given. (author). 14 refs. (Atomindex citation 19:059900)