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 Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 1, Pages 100–116 (Mi izv1608)

On the interconnection of local and global approximations by holomorphic functions

P. V. Paramonov

Abstract: It is proved that if a function $f\in\operatorname{Lip}(\alpha,X)$, $\alpha>2/3$, can be approximated locally outside its zero set by holomorphic functions, then it can be approximated also on the whole compact set $X$. This implies that if $f\in\operatorname{Lip}(\alpha,X)$, $\alpha>2/3$, and $f^2$ can be approximated by holomorphic functions on $X$, then so can $f$.
Bibliography: 5 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 20:1, 103–118

Bibliographic databases:

UDC: 517.5
MSC: Primary 30E10, 41A20; Secondary 30C85

Citation: P. V. Paramonov, “On the interconnection of local and global approximations by holomorphic functions”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982), 100–116; Math. USSR-Izv., 20:1 (1983), 103–118

Citation in format AMSBIB
\Bibitem{Par82} \by P.~V.~Paramonov \paper On the interconnection of local and global approximations by holomorphic functions \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1982 \vol 46 \issue 1 \pages 100--116 \mathnet{http://mi.mathnet.ru/izv1608} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=643896} \zmath{https://zbmath.org/?q=an:0519.30033} \transl \jour Math. USSR-Izv. \yr 1983 \vol 20 \issue 1 \pages 103--118 \crossref{https://doi.org/10.1070/IM1983v020n01ABEH001342} 

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This publication is cited in the following articles:
1. Anthony G. O'Farrell, “Rational approximation and weak analyticity. I”, Math Ann, 273:3 (1986), 375
2. P. V. Paramonov, “On the possibility of division and involution to a fractional power in the algebra of rational functions”, Math. USSR-Izv., 30:2 (1988), 385–393
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