Abstract:
This paper studies a variation of the equilibrium energy for a certain fairly general functional which appears naturally in the solution of many rational approximation problems of multi-valued analytic functions.
The main result of this work states that for the energy functional under consideration and a certain class of admissible compact sets, related to the function to be approximated, the corresponding stationary compact set is
fully characterized by the so-called $S$-property.
Bibliography: 38 titles.
Citation:
A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, “Variation of the equilibrium energy and the $S$-property of stationary compact sets”, Sb. Math., 202:12 (2011), 1831–1852
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\by A.~Mart{\'\i}nez-Finkelshtein, E.~A.~Rakhmanov, S.~P.~Suetin
\paper Variation of the equilibrium energy and the $S$-property of stationary compact sets
\jour Sb. Math.
\yr 2011
\vol 202
\issue 12
\pages 1831--1852
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Linking options:
https://www.mathnet.ru/eng/sm7854
https://doi.org/10.1070/SM2011v202n12ABEH004209
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This publication is cited in the following 29 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
Jacob S. Christiansen, Benjamin Eichinger, Olof Rubin, “Extremal Polynomials and Sets of Minimal Capacity”, Constr Approx, 2024
S. P. Suetin, “A direct proof of Stahl's theorem for a generic class of algebraic functions”, Sb. Math., 213:11 (2022), 1582–1596
Marco Bertola, Pavel Bleher, Roozbeh Gharakhloo, Kenneth T. -R. McLaughlin, Alexander Tovbis, Operator Theory: Advances and Applications, 289, Toeplitz Operators and Random Matrices, 2022, 151
V. N. Sorokin, “Hermite-Padé approximants to the Weyl function and its derivative for discrete measures”, Sb. Math., 211:10 (2020), 1486–1502
E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518
M. A. Lapik, D. N. Tulyakov, “On expanding neighborhoods of local universality of Gaussian unitary ensembles”, Proc. Steklov Inst. Math., 301 (2018), 170–179
V. N. Sorokin, “Multipoint Hermite–Padé approximants for three beta functions”, Trans. Moscow Math. Soc., 2018, 117–134
V. N. Sorokin, “On Multiple Orthogonal Polynomials for Three Meixner Measures”, Proc. Steklov Inst. Math., 298 (2017), 294–316
V. N. Sorokin, “Ob asimptoticheskikh rezhimakh sovmestnykh mnogochlenov Meiksnera”, Preprinty IPM im. M. V. Keldysha, 2016, 046, 32 pp.
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:SI (2016), 48–67
A. B. J. Kuijlaars, G. L. F. Silva, “S-curves in polynomial external fields”, J. Approx. Theory, 191 (2015), 1–37
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
V. I. Buslaev, “Capacity of a compact set in a logarithmic potential field”, Proc. Steklov Inst. Math., 290:1 (2015), 238–255
S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951
V. I. Buslaev, “An analogue of Polya's theorem for piecewise holomorphic functions”, Sb. Math., 206:12 (2015), 1707–1721
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
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
V. I. Buslaev, S. P. Suetin, “An extremal problem in potential theory”, Russian Math. Surveys, 69:5 (2014), 915–917
D. Huybrechs, A. B. J. Kuijlaars, N. Lejon, “Zero distribution of complex orthogonal polynomials with respect to exponential weights”, J. Approx. Theory, 184 (2014), 28–54
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