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Sovrem. Probl. Mat., 2003, Issue 1, Pages 83–106 (Mi spm4)  

This article is cited in 19 scientific papers (total in 20 papers)

Rational Approximations of Analytic Functions

A. A. Gonchar


Abstract: The paper provides an overview of the author's contribution to the theory of constructive rational approximations of analytic functions. The results presented are related to the convergence theory of Padé approximants and of more general rational interpolation processes, which significantly expand the classical theory's framework of continuous fractions, to inverse problems in the theory of Padé approximants, to the application of multipoint Padé approximants (solutions of Cauchy–Jacobi interpolation problem) in explorations connected with the rate of Chebyshev rational approximation of analytic functions and to the asymptotic properties of Padé–Hermite approximation for systems of Markov type functions.

DOI: https://doi.org/10.4213/spm4

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 2, S44–S57

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Citation: A. A. Gonchar, “Rational Approximations of Analytic Functions”, Sovrem. Probl. Mat., 1, Steklov Math. Institute of RAS, Moscow, 2003, 83–106; Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57

Citation in format AMSBIB
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\paper Rational Approximations of Analytic Functions
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\yr 2003
\vol 1
\pages 83--106
\publ Steklov Math. Institute of RAS
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2011
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\pages S44--S57
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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. D. V. Khristoforov, “On uniform approximation of elliptic functions by Padé approximants”, Sb. Math., 200:6 (2009), 923–941  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. I. Buslaev, “An analogue of Fabry's theorem for generalized Padé approximants”, Sb. Math., 200:7 (2009), 981–1050  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. A. P. Bulanov, “Iterated cyclic exponentials and power functions with extra-periodic first coefficients”, Sb. Math., 201:1 (2010), 23–55  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. 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
    6. A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of Meixner polynomials and Christoffel-Darboux kernels”, Trans. Moscow Math. Soc., 73 (2012), 67–106  mathnet  crossref  mathscinet  zmath  elib
    7. A. V. Komlov, S. P. Suetin, “An asymptotic formula for polynomials orthonormal with respect to a varying weight”, Trans. Moscow Math. Soc., 73 (2012), 139–159  mathnet  crossref  mathscinet  zmath  elib
    8. 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  mathnet  crossref  mathscinet  isi  elib
    9. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Cacoq J., de la Calle Ysern B., Lopez Lagomasino G., “Direct and Inverse Results on Row Sequences of Hermite-Pad, Approximants”, Constr. Approx., 38:1 (2013), 133–160  crossref  mathscinet  zmath  isi  elib  scopus
    11. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. 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  mathnet  crossref  crossref  isi  elib  elib
    13. 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  mathnet  crossref  crossref  isi  elib  elib
    14. 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
    15. N. R. Ikonomov, R. K. Kovacheva, S. P. Suetin, “Nuttall's integral equation and Bernshtein's asymptotic formula for a complex weight”, Izv. Math., 79:6 (2015), 1215–1234  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    16. 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
    17. 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
    18. G. López Lagomasino, Y. Zaldivar Gerpe, “Inverse Results on Row Sequences of Hermite–Padé Approximation”, Proc. Steklov Inst. Math., 298 (2017), 152–169  mathnet  crossref  crossref  isi  elib
    19. A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Proc. Steklov Inst. Math., 298 (2017), 317–333  mathnet  crossref  crossref  isi  elib
    20. 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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