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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 2, Pages 412–420 (Mi izv1301)  

This article is cited in 1 scientific paper (total in 1 paper)

On the possibility of division and involution to a fractional power in the algebra of rational functions

P. V. Paramonov


Abstract: Suppose that a function $f(z)$ satisfies a Lipschitz condition with an arbitrary positive element on a compact set $X$ in $\mathbf C$ and can be uniformly approximated on $X$ by rational functions. If $q>1$ and some branch of $(f(z))^q$ is continuous on $X$, then this branch can also be approximated on $X$ by rational functions. Also, an example is given of a compact set $X$ and two functions $f(z)$ and $g(z)$ uniformly approximable on $X$ by rational functions and with ratio $g(z)/f(z)$ naturally (uniquely) defined and continuous on $X$ but not approximable by rational functions.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 30:2, 385–393

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A20, 46J10; Secondary 30C15, 41A46
Received: 20.02.1985

Citation: P. V. Paramonov, “On the possibility of division and involution to a fractional power in the algebra of rational functions”, Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987), 412–420; Math. USSR-Izv., 30:2 (1988), 385–393

Citation in format AMSBIB
\Bibitem{Par87}
\by P.~V.~Paramonov
\paper On~the possibility of division and involution to a~fractional power in the algebra of rational functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 2
\pages 412--420
\mathnet{http://mi.mathnet.ru/izv1301}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=897005}
\zmath{https://zbmath.org/?q=an:0643.30036}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 30
\issue 2
\pages 385--393
\crossref{https://doi.org/10.1070/IM1988v030n02ABEH001019}


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    This publication is cited in the following articles:
    1. Gilev S.D., “Experimental study of shock-wave magnetic cumulation”, Combustion Explosion and Shock Waves, 44:2 (2008), 218–227  crossref  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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