Rational mnemofunctions on R

Abstract

The subspace of rational distributions was considered it this paper. Distribution is called rational if it has analytical representation f = (f+, f-) where functions f+ and f- are proper rational functions. The embedding of the rational distributions subspace into the rational mnemofunctions algebra on was built by the mean of mapping Ra(f)=fε(x)=f+(x+iε)-f-(x-iε). A complete description of this algebra was given. Its generators were singled out; the multiplication rule of distributions in this algebra was formulated explicitly. Known cases when product of distributions is a distribution were analyzed by the terms of rational mnemofunctions theory. The conditions under which the product of arbitrary rational distributions is associated with a distribution were formulated.

Keywords

• mnemofunction
• analytical representation of distribution
• algebra of rational mnemofunctions