Rational mnemofunctions on R - Shahava, Tatsiana G. (Journal of the Belarusian State University. Mathematics and Informatics, 2019)
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