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 Mat. Sb. (N.S.), 1974, Volume 93(135), Number 2, Pages 314–324 (Mi msb2975)

Expansions in series and the rate of rational approximations for holomorphic functions with analytic singularities

E. M. Chirka

Abstract: It is proved that for functions holomorphic in the complement of an analytic subset of $\mathbf C^N$ the best rational approximation converges faster than any geometric progression.
Bibliography: 3 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 22:2, 323–332

Bibliographic databases:

Document Type: Article
UDC: 517.55
MSC: Primary 32A10, 32A05; Secondary 32E30

Citation: E. M. Chirka, “Expansions in series and the rate of rational approximations for holomorphic functions with analytic singularities”, Mat. Sb. (N.S.), 93(135):2 (1974), 314–324; Math. USSR-Sb., 22:2 (1974), 323–332

Citation in format AMSBIB
\Bibitem{Chi74} \by E.~M.~Chirka \paper Expansions in series and the rate of rational approximations for holomorphic functions with analytic singularities \jour Mat. Sb. (N.S.) \yr 1974 \vol 93(135) \issue 2 \pages 314--324 \mathnet{http://mi.mathnet.ru/msb2975} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=590075} \zmath{https://zbmath.org/?q=an:0286.32002} \transl \jour Math. USSR-Sb. \yr 1974 \vol 22 \issue 2 \pages 323--332 \crossref{https://doi.org/10.1070/SM1974v022n02ABEH001695} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. A. Gonchar, “A local condition for the single-valuedness of analytic functions of several variables”, Math. USSR-Sb., 22:2 (1974), 305–322
2. E. M. Chirka, “Rational approximations of holomorphic functions with singularities of finite order”, Math. USSR-Sb., 29:1 (1976), 123–138
3. A. S. Sadullaev, “Plurisubharmonic measures and capacities on complex manifolds”, Russian Math. Surveys, 36:4 (1981), 61–119
4. A. S. Sadullaev, “Rational approximation and pluripolar sets”, Math. USSR-Sb., 47:1 (1984), 91–113
5. A. Cuyt, K.A. Driver, D.S. Lubinsky, “A direct approach to convergence of multivariate, nonhomogeneous, Padé approximants”, Journal of Computational and Applied Mathematics, 69:2 (1996), 353
6. A. Cuyt, K. Driver, D.S. Lubinsky, “Nuttall-Pommerenke theorems for homogeneous Padé approximants”, Journal of Computational and Applied Mathematics, 67:1 (1996), 141
7. Bloom T., “On the Convergence in Capacity of Rational Approximants”, Constr. Approx., 17:1 (2001), 91–102
8. A. S. Sadullaev, “Pluriharmonic continuation in a fixed direction”, Sb. Math., 196:5 (2005), 765–775
9. Nguyen Quang Dieu, “Weak Runge pairs in”, Journal of Mathematical Analysis and Applications, 327:1 (2007), 71
10. Nguyen Quang Dieu, Tang Van Long, “A New Class of Pluripolar Sets”, Ann. Pol. Math., 90:3 (2007), 229–245
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