The Products δn²(x), δ(x). X^-n, ϴ(x). X^-n, etc. in the Class of the Asymptotic Functions

Todor D. Todorov, Institute of Nuclear Research and Nuclear Energy, Bulgaria

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Copyright © 1985 Heron Press Limited.

NOTE: At the time of publication, the author Todor D. Todorov was not yet affiliated with Cal Poly.

Abstract

Several products like δⁿ(x), δ(x)ϴ(x), δ^(m)(x). X^-n, ϴ(x). X^-n, etc., where δ(x), ϴ(x), X^-n, etc., are kernels of the corresponding Schwartz distributions, are studied in the framework of the class of the asymptotic functions F₀ introduced in a previous paper [11]. In some particular cases many formulae are derived and several examples are presented. The work is of mathematical type but its motivations lie in some problems in quantum theory. It is closely connected with a series of previous works [1 - 11] and first of all with [11].