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Mat. Sb., 2015, Volume 206, Number 2, Pages 5–30 (Mi msb8428)  

This article is cited in 18 scientific papers (total in 18 papers)

Convergence of $m$-point Padé approximants of a tuple of multivalued analytic functions

V. I. Buslaevab

a Steklov Mathematical Institute of Russian Academy of Sciences
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: We prove the convergence of $m$-point Padé approximants of an $m$-tuple of holomorphic germs that admit analytic continuation along all paths in the extended complex plane that do not pass through a finite set of points. This result extends Stahl's theorem from the case $m=1$ to the case of an arbitrary $m\in\mathbb N$.
Bibliography: 15 titles.

Keywords: rational approximation, orthogonal polynomials, Padé approximants, convergence in capacity, limiting distribution of poles.

Funding Agency Grant Number
Russian Science Foundation 14-21-00025
This research was supported by the Russian Science Foundation under grant no. 14-21-00025.


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English version:
Sbornik: Mathematics, 2015, 206:2, 175–200

Bibliographic databases:

UDC: 517.53
MSC: 41A21, 30E10, 42C05
Received: 28.07.2014

Citation: V. I. Buslaev, “Convergence of $m$-point Padé approximants of a tuple of multivalued analytic functions”, Mat. Sb., 206:2 (2015), 5–30; Sb. Math., 206:2 (2015), 175–200

Citation in format AMSBIB
\by V.~I.~Buslaev
\paper Convergence of $m$-point Pad\'e approximants of a~tuple of multivalued analytic functions
\jour Mat. Sb.
\yr 2015
\vol 206
\issue 2
\pages 5--30
\jour Sb. Math.
\yr 2015
\vol 206
\issue 2
\pages 175--200

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    This publication is cited in the following articles:
    1. V. I. Buslaev, “Capacity of a compact set in a logarithmic potential field”, Proc. Steklov Inst. Math., 290:1 (2015), 238–255  mathnet  crossref  crossref  isi  elib  elib
    2. S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. V. I. Buslaev, “An analogue of Polya's theorem for piecewise holomorphic functions”, Sb. Math., 206:12 (2015), 1707–1721  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. A. V. Komlov, S. P. Suetin, “Distribution of the zeros of Hermite–Padé polynomials”, Russian Math. Surveys, 70:6 (2015), 1179–1181  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. V. I. Buslaev, “An analog of Gonchar's theorem for the $m$-point version of Leighton's conjecture”, Proc. Steklov Inst. Math., 293 (2016), 127–139  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. 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
    7. S. P. Suetin, “Zero distribution of Hermite–Padé polynomials and localization of branch points of multivalued analytic functions”, Russian Math. Surveys, 71:5 (2016), 976–978  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. V. I. Buslaev, “The Capacity of the Rational Preimage of a Compact Set”, Math. Notes, 100:6 (2016), 781–790  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. 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 (2016), 48–67  mathnet  crossref  mathscinet  zmath  isi  scopus
    10. S. P. Suetin, “On the distribution of the zeros of the Hermite–Padé polynomials for a quadruple of functions”, Russian Math. Surveys, 72:2 (2017), 375–377  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. A. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka, “Hermite–Padé approximants for meromorphic functions on a compact Riemann surface”, Russian Math. Surveys, 72:4 (2017), 671–706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. V. I. Buslaev, “On the Van Vleck Theorem for Limit-Periodic Continued Fractions of General Form”, Proc. Steklov Inst. Math., 298 (2017), 68–93  mathnet  crossref  crossref  mathscinet  isi  elib
    13. V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    14. V. I. Buslaev, “On Singular points of Meromorphic Functions Determined by Continued Fractions”, Math. Notes, 103:4 (2018), 527–536  mathnet  crossref  crossref  mathscinet  isi  elib
    15. E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. 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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    17. V. I. Buslaev, “On a lower bound for the rate of convergence of multipoint Padé approximants of piecewise analytic functions”, Izv. Math., 85:3 (2021), 351–366  mathnet  crossref  crossref  isi  elib
    18. M. L. Yattselev, “Skhodimost dvukhtochechnykh approksimatsii Pade k kusochno golomorfnym funktsiyam”, Matem. sb., 212:11 (2021), 128–164  mathnet  crossref
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