Abstract:
A theorem is proved on the uniform convergence of diagonal Padé approximants for Stieltjes type meromorphic functions (with a finite number of poles).
Bibliography: 13 titles.
Citation:
G. L. Lopes, “Convergence of Padé approximants of Stieltjes type meromorphic functions and comparative asymptotics for orthogonal polynomials”, Math. USSR-Sb., 64:1 (1989), 207–227
\Bibitem{Lop88}
\by G.~L.~Lopes
\paper Convergence of Pad\'e approximants of Stieltjes type meromorphic functions and comparative asymptotics for orthogonal polynomials
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 1
\pages 207--227
\mathnet{http://mi.mathnet.ru/eng/sm1737}
\crossref{https://doi.org/10.1070/SM1989v064n01ABEH003303}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=954925}
\zmath{https://zbmath.org/?q=an:0669.30026|0658.30029}
Linking options:
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https://doi.org/10.1070/SM1989v064n01ABEH003303
https://www.mathnet.ru/eng/sm/v178/i2/p206
This publication is cited in the following 33 articles:
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L.G. González Ricardo, G. López Lagomasino, S. Medina Peralta, “On the convergence of multi-level Hermite-Padé approximants”, Physica D: Nonlinear Phenomena, 440 (2022), 133487
Duenas H. Fuentes E. Garza L.E., “Matrix Uvarov Transformation on the Unit Circle: Asymptotic Properties”, Bull. Malays. Math. Sci. Soc., 44:1 (2021), 279–315
Fidalgo U. Lopez Lagomasino G. Medina Peralta S., “Asymptotic of Cauchy Biorthogonal Polynomials”, Mediterr. J. Math., 17:1 (2020), 22
Ricardo Gonzalez L.G. Lopez Lagomasino G. Peralta S.M., “On the Convergence of Multi-Level Hermite-Pade Approximants For a Class of Meromorphic Functions”, Mediterr. J. Math., 17:5 (2020), 149
G. López Lagomasino, S. Medina Peralta, “On the convergence of type I Hermite–Padé approximants for rational perturbations of a Nikishin system”, Journal of Computational and Applied Mathematics, 2015
G. López Lagomasino, S. Medina Peralta, U. Fidalgo Prieto, “Hermite-Padé approximation for certain systems of meromorphic functions”, Sb. Math., 206:2 (2015), 225–241
Doron S. Lubinsky, Analytic Number Theory, Approximation Theory, and Special Functions, 2014, 561
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
U. Fidalgo Prieto, A. López García, G. López Lagomasino, V. N. Sorokin, “Mixed Type Multiple Orthogonal Polynomials for Two Nikishin Systems”, Constr Approx, 2010
de la Calle Ysern B., “A Walk through Approximation Theory”, Recent Trends in Orthogonal Polynomials and Approximation Theory, Contemporary Mathematics, 507, 2010, 25–86
Baratchart, L, “Multipoint Pade approximants to complex Cauchy transforms with polar singularities”, Journal of Approximation Theory, 156:2 (2009), 187
Herbert Duenas, Francisco Marcellan, Eduardo Prianes, “Perturbations of Laguerre-Hahn functional: modification by the derivative of a Dirac delta”, Integral Transforms & Special Functions, 20:1 (2009), 59
Garcia, AL, “Ratio asymptotic of Hermite-Pade orthogonal polynomials for Nikishin systems. II”, Advances in Mathematics, 218:4 (2008), 1081
B. P. Osilenker, “An Extremal Problem for Algebraic Polynomials in the Symmetric Discrete Gegenbauer–Sobolev Space”, Math. Notes, 82:3 (2007), 366–379
Rolania, DB, “Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures”, Journal of Approximation Theory, 139:1–2 (2006), 223
Boris P. Osilenker, “Generalized trace formula and asymptotics of the averaged Turan determinant for polynomials orthogonal with a discrete Sobolev inner product”, Journal of Approximation Theory, 141:1 (2006), 70
A. I. Aptekarev, G. López Lagomasino, I. Alvarez Rocha, “Ratio asymptotics of Hermite–Padé polynomials for Nikishin systems”, Sb. Math., 196:8 (2005), 1089–1107
C. Díaz-Mendoza, P. González-Vera, R. Orive, “On the convergence of two-point partial Padé approximants for meromorphic functions of Stieltjes type”, Applied Numerical Mathematics, 53:1 (2005), 39
A. Bultheel, P. González-Vera, E. Hendriksen, O. Njåstad, “Determinacy of a rational moment problem”, Journal of Computational and Applied Mathematics, 133:1-2 (2001), 241
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