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Journal of the Belarusian State University. Mathematics and Informatics, 2019, Volume 2, Pages 6–17
DOI: https://doi.org/10.33581/2520-6508-2019-2-6-17
(Mi bgumi91)
 

This article is cited in 4 scientific papers (total in 4 papers)

Real, Complex and Functional analysis

Rational mnemofunctions on $\mathbb{R}$

T. G. Shahava

Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
Full-text PDF (580 kB) Citations (4)
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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 $f^{\pm}$ are proper rational functions. The embedding of the rational distributions subspace into the rational mnemofunctions algebra on $\mathbb{R}$ was built by the mean of mapping $R_{a}(f)=f_{\varepsilon}(x)=f^{+}(x+i\varepsilon) - f^{-}(x-i\varepsilon)$. 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.
Received: 22.01.2019
Document Type: Article
UDC: 517.9
Language: Russian
Citation: T. G. Shahava, “Rational mnemofunctions on $\mathbb{R}$”, Journal of the Belarusian State University. Mathematics and Informatics, 2 (2019), 6–17
Citation in format AMSBIB
\Bibitem{Sha19}
\by T.~G.~Shahava
\paper Rational mnemofunctions on $\mathbb{R}$
\jour Journal of the Belarusian State University. Mathematics and Informatics
\yr 2019
\vol 2
\pages 6--17
\mathnet{http://mi.mathnet.ru/bgumi91}
\crossref{https://doi.org/10.33581/2520-6508-2019-2-6-17}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Journal of the Belarusian State University. Mathematics and Informatics
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