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

This article is cited in 10 scientific papers (total in 10 papers)

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.

Full text: PDF file (1117 kB)
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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
Received: 27.08.1973

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  mathnet  crossref  mathscinet  zmath
    2. E. M. Chirka, “Rational approximations of holomorphic functions with singularities of finite order”, Math. USSR-Sb., 29:1 (1976), 123–138  mathnet  crossref  mathscinet  zmath  isi
    3. A. S. Sadullaev, “Plurisubharmonic measures and capacities on complex manifolds”, Russian Math. Surveys, 36:4 (1981), 61–119  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. S. Sadullaev, “Rational approximation and pluripolar sets”, Math. USSR-Sb., 47:1 (1984), 91–113  mathnet  crossref  mathscinet  zmath
    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  crossref
    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  crossref
    7. Bloom T., “On the Convergence in Capacity of Rational Approximants”, Constr. Approx., 17:1 (2001), 91–102  isi
    8. A. S. Sadullaev, “Pluriharmonic continuation in a fixed direction”, Sb. Math., 196:5 (2005), 765–775  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Nguyen Quang Dieu, “Weak Runge pairs in”, Journal of Mathematical Analysis and Applications, 327:1 (2007), 71  crossref
    10. Nguyen Quang Dieu, Tang Van Long, “A New Class of Pluripolar Sets”, Ann. Pol. Math., 90:3 (2007), 229–245  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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