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This article is cited in 17 scientific papers (total in 17 papers)
Convergence of multipoint Padé approximants of piecewise analytic functions
V. I. Buslaev
Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
The behaviour as $n\to\infty$ of multipoint Padé approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Padé approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Padé approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points.
Bibliography: 11 titles.
Keywords:
rational approximation, orthogonal polynomials, Padé approximants, convergence in capacity, asymptotic behaviour of poles.
DOI:
https://doi.org/10.4213/sm8099
 Full text:
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English version:
Sbornik: Mathematics, 2013, 204:2, 190–222
Bibliographic databases:
     
UDC:
517.53
MSC: Primary 41A21; Secondary 31A15
Received: 26.12.2011 and 06.12.2012
Citation:
V. I. Buslaev, “Convergence of multipoint Padé approximants of piecewise analytic functions”, Mat. Sb., 204:2 (2013), 39–72; Sb. Math., 204:2 (2013), 190–222
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/msb8099https://doi.org/10.4213/sm8099 http://mi.mathnet.ru/eng/msb/v204/i2/p39
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This publication is cited in the following articles:
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V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Method of interior variations and existence of $S$-compact sets”, Proc. Steklov Inst. Math., 279 (2012), 25–51
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A. V. Komlov, S. P. Suetin, “An asymptotic formula for a two-point analogue of Jacobi polynomials”, Russian Math. Surveys, 68:4 (2013), 779–781
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E. A. Rakhmanov, S. P. Suetin, “The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system”, Sb. Math., 204:9 (2013), 1347–1390
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V. I. Buslaev, S. P. Suetin, “Existence of compact sets with minimum capacity in problems of rational approximation of multivalued analytic functions”, Russian Math. Surveys, 69:1 (2014), 159–161
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R. K. Kovacheva, S. P. Suetin, “Distribution of zeros of the Hermite–Padé polynomials for a system of three functions, and the Nuttall condenser”, Proc. Steklov Inst. Math., 284 (2014), 168–191
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V. I. Buslaev, S. P. Suetin, “An extremal problem in potential theory”, Russian Math. Surveys, 69:5 (2014), 915–917
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A. V. Komlov, S. P. Suetin, “Strong asymptotics of two-point Padé approximants for power-like multivalued functions”, Dokl. Math., 89:2 (2014), 165–168
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V. I. Buslaev, “Convergence of $m$-point Padé approximants of a tuple of multivalued analytic functions”, Sb. Math., 206:2 (2015), 175–200
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V. I. Buslaev, S. P. Suetin, “On equilibrium problems related to the distribution of zeros of the Hermite–Padé polynomials”, Proc. Steklov Inst. Math., 290:1 (2015), 256–263
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V. I. Buslaev, “Capacity of a compact set in a logarithmic potential field”, Proc. Steklov Inst. Math., 290:1 (2015), 238–255
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S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951
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V. I. Buslaev, “An analogue of Polya's theorem for piecewise holomorphic functions”, Sb. Math., 206:12 (2015), 1707–1721
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A. V. Komlov, S. P. Suetin, “Distribution of the zeros of Hermite–Padé polynomials”, Russian Math. Surveys, 70:6 (2015), 1179–1181
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V. I. Buslaev, S. P. Suetin, “On the existence of compacta of minimal capacity in the theory of rational approximation of multi-valued analytic functions”, J. Approx. Theory, 206:SI (2016), 48–67
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A. Martinez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, “Asymptotics of type I Hermite–Padé polynomials for semiclassical functions”, Modern trends in constructive function theory, Contemp. Math., 661, ed. D. Hardin, D. Lubinsky, B. Simanek, Amer. Math. Soc., Providence, RI, 2016, 199–228
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E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518
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S. P. Suetin, “On a new approach to the problem of distribution of zeros of Hermite–Padé polynomials for a Nikishin system”, Proc. Steklov Inst. Math., 301 (2018), 245–261
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