Rational mnemofunctions on R

• Main Author: Tatsiana G. Shahava
• Format: Article
• Language: Belarusian
• Published: Belarusian State University 2019-07-01
• Series: Журнал Белорусского государственного университета: Математика, информатика
• Subjects: mnemofunction; analytical representation of distribution; algebra of rational mnemofunctions
• Online Access: https://journals.bsu.by/index.php/mathematics/article/view/946

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.