Журнал Белорусского государственного университета: Математика, информатика (Jul 2019)

Rational mnemofunctions on R

  • Tatsiana G. Shahava

DOI
https://doi.org/10.33581/2520-6508-2019-2-6-17
Journal volume & issue
no. 2
pp. 6 – 17

Abstract

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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.

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