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Mat. Sb. (N.S.), 1972, Volume 89(131), Number 1(9), Pages 148–164 (Mi msb3223)  

This article is cited in 24 scientific papers (total in 26 papers)

A local condition of single-valuedness of analytic functions

A. A. Gonchar


Abstract: In this paper a local condition of single-valuedness of an analytic function in its natural domain of existence is obtained. The condition is formulated in terms of rational approximations.
Bibliography: 9 titles.

Full text: PDF file (1538 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1972, 18:1, 151–167

Bibliographic databases:

UDC: 517.53
MSC: Primary 30A82; Secondary 30A14
Received: 17.02.1972

Citation: A. A. Gonchar, “A local condition of single-valuedness of analytic functions”, Mat. Sb. (N.S.), 89(131):1(9) (1972), 148–164; Math. USSR-Sb., 18:1 (1972), 151–167

Citation in format AMSBIB
\Bibitem{Gon72}
\by A.~A.~Gonchar
\paper A local condition of single-valuedness of analytic functions
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 89(131)
\issue 1(9)
\pages 148--164
\mathnet{http://mi.mathnet.ru/msb3223}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=322144}
\zmath{https://zbmath.org/?q=an:0247.30033}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 18
\issue 1
\pages 151--167
\crossref{https://doi.org/10.1070/SM1972v018n01ABEH001622}


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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, “On the convergence of Padé approximants”, Math. USSR-Sb., 21:1 (1973), 155–166  mathnet  crossref  mathscinet  zmath
    2. 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
    3. E. M. Chirka, “Expansions in series and the rate of rational approximations for holomorphic functions with analytic singularities”, Math. USSR-Sb., 22:2 (1974), 323–332  mathnet  crossref  mathscinet  zmath
    4. A. A. Gonchar, “The rate of rational approximation and the property of single-valuedness of an analytic function in the neighborhood of an isolated singular point”, Math. USSR-Sb., 23:2 (1974), 254–270  mathnet  crossref  mathscinet  zmath
    5. 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
    6. Johan Karlsson, “Rational interpolation and best rational approximation”, Journal of Mathematical Analysis and Applications, 53:1 (1976), 38  crossref
    7. A. A. Gonchar, K. N. Lungu, “Poles of diagonal Padé approximants and the analytic continuation of functions”, Math. USSR-Sb., 39:2 (1981), 255–266  mathnet  crossref  mathscinet  zmath  isi
    8. A. S. Sadullaev, “Plurisubharmonic measures and capacities on complex manifolds”, Russian Math. Surveys, 36:4 (1981), 61–119  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. S. Sadullaev, “Rational approximation and pluripolar sets”, Math. USSR-Sb., 47:1 (1984), 91–113  mathnet  crossref  mathscinet  zmath
    10. A. S. Sadullaev, “A criterion for rapid rational approximation in $\mathbf C^n$”, Math. USSR-Sb., 53:1 (1986), 271–281  mathnet  crossref  mathscinet  zmath
    11. Gonchar A., “Rational Approximation of Analytic-Functions”, 1043, 1984, 471–474  isi
    12. D. S. Lubinsky, “Distribution of poles of diagonal rational approximants to functions of fast rational approximability”, Constr Approx, 7:1 (1991), 501  crossref  mathscinet  zmath  isi
    13. V. A. Prokhorov, “Rational approximation of analytic functions”, Russian Acad. Sci. Sb. Math., 78:1 (1994), 139–164  mathnet  crossref  mathscinet  zmath  isi
    14. 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
    15. Herbert Stahl, “Spurious poles in Padé approximation”, Journal of Computational and Applied Mathematics, 99:1-2 (1998), 511  crossref
    16. Bloom T., “On the Convergence in Capacity of Rational Approximants”, Constr. Approx., 17:1 (2001), 91–102  isi
    17. Baratchart L. Stahl H. Wielonsky F., “Asymptotic Uniqueness of Best Rational Approximants of Given Degree to Markov Functions in l-2 of the Circle”, Constr. Approx., 17:1 (2001), 103–138  isi
    18. A. A. Bolibrukh, A. G. Vitushkin, V. S. Vladimirov, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, A. G. Sergeev, P. L. Ul'yanov, L. D. Faddeev, E. M. Chirka, “Andrei Aleksandrovich Gonchar (on his 70th birthday)”, Russian Math. Surveys, 57:1 (2002), 191–198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    19. Kovacheva R., Lawrynowicz J., “An Analogue of Montel's Theorem for Some Classes of Rational Functions”, Czech. Math. J., 52:3 (2002), 483–498  crossref  isi
    20. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57  mathnet  crossref  crossref  mathscinet  zmath  isi
    21. H. -P. Blatt, “The impact of poles on the convergence of best rational approximants”, J Contemp Mathemat Anal, 44:4 (2009), 243  crossref  isi
    22. H.-P. Blatt, R. Grothmann, R.K. Kovacheva, “Regions of meromorphy and value distribution of geometrically converging rational functions”, Journal of Mathematical Analysis and Applications, 382:1 (2011), 66  crossref
    23. A. I. Aptekarev, G. López Lagomasino, E. B. Saff, V. Totik, H. Stahl, “Andrei Aleksandrovich Gonchar (on his 80th birthday)”, Russian Math. Surveys, 66:6 (2011), 1209–1216  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    24. E. A. Rakhmanov, “The Gonchar-Stahl $\rho^2$-theorem and associated directions in the theory of rational approximations of analytic functions”, Sb. Math., 207:9 (2016), 1236–1266  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    25. A. Sadullaev, Z. Ibragimov, “The class $R$ and finely analytic functions”, Sb. Math., 209:8 (2018), 1234–1247  mathnet  crossref  crossref  adsnasa  isi  elib
    26. A. Sadullaev, “Prodolzhenie analiticheskikh i plyurigarmonicheskikh funktsii po zadannomu napravleniyu metodom E. M. Chirki (obzor)”, Sovremennye problemy matematiki i fiziki, SMFN, 65, no. 1, Rossiiskii universitet druzhby narodov, M., 2019, 83–94  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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