Auotomodeling rational mnemofunctions and their link to an analytical representation of distributions
https://doi.org/10.29235/1561-2430-2019-55-3-288-298
Abstract
Mnemofunctions of the form f(x/ε), where f is the proper rational function without singularities on the real line, are considered in this article. Such mnemofunctions are called automodeling rational mnemofunctions. They possess the following fine properties: asymptotic expansions in the space of distributions can be written in explicit form and the asymptotic expansion of the product of such mnemofunctions is uniquely determined by the expansions of multiplicands.
Partial fraction decomposition of automodeling rational mnemofunctions generates the so-called sloped analytical representation of a distribution, i.e. the representation of a distribution by a jump of the boundary values of the functions analytical in upper and lower half-planes. Sloped analytical representation is similar to the classical Cauchy analytical representation, but its structure is more complicated. The multiplication rule of such representations is described in this article.
About the Author
T. R. Shahava
Belarusian State University
Belarus
Belarus
Tatsiana R. Shahava – Postgraduate Student
4, Nezavisimosti Ave., 220030, Minsk, Republic of Belarus
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