Geodesic
Rational mnemofunctions on $\mathbb{R}$
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2019), pp. 6-17

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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 $f^{\pm}$ 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. 
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     title = {Rational mnemofunctions on $\mathbb{R}$},
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T. G. Shahava. Rational mnemofunctions on $\mathbb{R}$. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2019), pp. 6-17. http://geodesic.mathdoc.fr/item/BGUMI_2019_2_a0/