Rational mnemofunctions on R

Authors

Keywords:

mnemofunction, analytical representation of distribution, algebra of rational mnemofunctions

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.

Author Biography

  • Tatsiana G. Shahava, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    postgraduate student at the department of functional analysis and analytical economics, faculty of mechanics and mathematics

References

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Published

2019-07-26

Issue

No. 2 (2019): Journal of the Belarusian State University. Mathematics and Informatics

Section

Real, Complex and Functional Analysis

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How to Cite

[1]
Shahava, T.G. 2019. Rational mnemofunctions on R. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Jul. 2019), 6–17. DOI:https://doi.org/10.33581/2520-6508-2019-2-6-17.