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,f2], where f is a multivalued function in the so-called Laguerre class 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.
\Bibitem{Sue15}
\by S.~P.~Suetin
\paper Distribution of the zeros of Pad\'e polynomials and analytic continuation
\jour Russian Math. Surveys
\yr 2015
\vol 70
\issue 5
\pages 901--951
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https://www.mathnet.ru/eng/rm9675
https://doi.org/10.1070/RM2015v070n05ABEH004966
https://www.mathnet.ru/eng/rm/v70/i5/p121
This publication is cited in the following 47 articles:
S. P. Suetin, “O skalyarnykh podkhodakh k izucheniyu predelnogo raspredeleniya nulei mnogochlenov Ermita–Pade dlya sistemy Nikishina”, UMN, 80:1(481) (2025), 85–152
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Lubinsky D.S., “Distribution of Eigenvalues of Toeplitz Matrices With Smooth Entries”, Linear Alg. Appl., 633 (2022), 332–365
E. A. Rakhmanov, S. P. Suetin, “Approksimatsii Chebysheva–Pade dlya mnogoznachnykh funktsii”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 319–344
A. P. Starovoitov, N. V. Ryabchenko, “O determinantnykh predstavleniyakh mnogochlenov Ermita–Pade”, Tr. MMO, 83, no. 1, MTsNMO, M., 2022, 17–35
A. I. Aptekarev, M. L. Yattselev, “Gipoteza Gonchara–Chudnovskikh i funktsionalnyi analog teoremy Tue–Zigelya–Rota”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 297–318
E. A. Rakhmanov, S. P. Suetin, “Chebyshev–Padé approximants for multivalued functions”, Trans. Moscow Math. Soc., –
A. P. Starovoitov, N. V. Ryabchenko, “On determinant representations of Hermite–Padé polynomials”, Trans. Moscow Math. Soc., –
A. I. Aptekarev, M. Yattselev, “The Gonchar–Chudnovskies conjecture and a functional analogue of the Thue–Siegel–Roth theorem”, Trans. Moscow Math. Soc., 2022, –
Trefethen L.N., Nakatsukasa Yu., Weideman J.A.C., “Exponential Node Clustering At Singularities For Rational Approximation, Quadrature, and Pdes”, Numer. Math., 147:1 (2021), 227–254
D. S. Lubinsky, “On uniform convergence of diagonal multipoint pade approximants for entire functions”, Constr. Approx., 49:1 (2019), 149–174
E. A. Karabut, A. G. Petrov, E. N. Zhuravleva, “Semi-analytical study of the voinovs problem”, Eur. J. Appl. Math., 30:2 (2019), 298–337
A. Gopal, L. N. Trefethen, “Representation of conformal maps by rational functions”, Numer. Math., 142:2 (2019), 359–382
Doron S. Lubinsky, Applied and Numerical Harmonic Analysis, Topics in Classical and Modern Analysis, 2019, 241
V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205
V. I. Buslaev, “On Singular points of Meromorphic Functions Determined by Continued Fractions”, Math. Notes, 103:4 (2018), 527–536
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
S. P. Suetin, “Distribution of the zeros of Hermite–Padé polynomials for a complex Nikishin system”, Russian Math. Surveys, 73:2 (2018), 363–365
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