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Uspekhi Mat. Nauk, 2015, Volume 70, Issue 5(425), Pages 121–174 (Mi umn9675)  

This article is cited in 33 scientific papers (total in 33 papers)

Distribution of the zeros of Padé polynomials and analytic continuation

S. P. Suetin

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: The problem of analytic continuation of a multivalued analytic function with finitely many branch points on the Riemann sphere is discussed. The focus is on Padé approximants: classical (one-point) Padé approximants, multipoint Padé approximants, and Hermite–Padé approximants. The main result is a theorem on the distribution of zeros and the convergence of the Hermite–Padé approximants for a system $[1,f,f^2]$, where $f$ is a multivalued function in the so-called Laguerre class $\mathscr{L}$.
Bibliography: 128 titles.

Keywords: analytic continuation, continued fractions, orthogonal polynomials, rational approximants, Padé polynomials, Hermite–Padé polynomials, distribution of zeros, GRS-method, convergence in capacity.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


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English version:
Russian Mathematical Surveys, 2015, 70:5, 901–951

Bibliographic databases:

UDC: 517.53
MSC: Primary 30E10, 30B40, 41A20, 41A21; Secondary 12H05, 31A15
Received: 30.06.2015

Citation: S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Uspekhi Mat. Nauk, 70:5(425) (2015), 121–174; Russian Math. Surveys, 70:5 (2015), 901–951

Citation in format AMSBIB
\by S.~P.~Suetin
\paper Distribution of the zeros of Pad\'e polynomials and analytic continuation
\jour Uspekhi Mat. Nauk
\yr 2015
\vol 70
\issue 5(425)
\pages 121--174
\jour Russian Math. Surveys
\yr 2015
\vol 70
\issue 5
\pages 901--951

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    This publication is cited in the following articles:
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    2. A. V. Astafieva, A. P. Starovoitov, “Hermite-Padé approximation of exponential functions”, Sb. Math., 207:6 (2016), 769–791  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. 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
    4. 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
    5. 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
    6. 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
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    9. M. V. Sidortsov, N. A. Starovoitova, A. P. Starovoitov, “Ob asimptotike approksimatsii Ermita–Pade vtorogo roda dlya eksponentsialnykh funktsii s kompleksnymi mnozhitelyami v pokazatelyakh eksponent”, PFMT, 2017, no. 1(30), 73–77  mathnet
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    11. M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2017, no. 2(31), 69–74  mathnet
    12. A. P. Starovoitov, “Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions”, Math. Notes, 102:2 (2017), 277–288  mathnet  crossref  crossref  mathscinet  isi  elib
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    18. E. A. Karabut, A. G. Petrov, E. N. Zhuravleva, “Semi-analytical investigation of unsteady free-boundary flows”, Application of Mathematics in Technical and Natural Sciences, AIP Conf. Proc., 1895, no. 1, Amer. Inst. Phys., 2017, 120006  crossref  isi  scopus
    19. V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    20. 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
    21. M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Skorost skhodimosti kvadratichnykh approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2018, no. 1(34), 71–78  mathnet
    22. S. P. Suetin, “Distribution of the zeros of Hermite–Padé polynomials for a complex Nikishin system”, Russian Math. Surveys, 73:2 (2018), 363–365  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    23. 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
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