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Trudy Mat. Inst. Steklova, 2012, Volume 279, Pages 31–58 (Mi tm3428)  

This article is cited in 18 scientific papers (total in 18 papers)

Method of interior variations and existence of $S$-compact sets

V. I. Buslaeva, A. Martínez-Finkelshteinb, S. P. Suetina

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Universidad de Almería, Almería, Spain

Abstract: The variation of equilibrium energy is analyzed for three different functionals that naturally arise in solving a number of problems in the theory of constructive rational approximation of multivalued analytic functions. The variational approach is based on the relationship between the variation of the equilibrium energy and the equilibrium measure. In all three cases the following result is obtained: for the energy functional and the class of admissible compact sets corresponding to the problem, the arising stationary compact set is fully characterized by a certain symmetry property.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00330
Ministry of Education and Science of the Russian Federation NSh-4664.2012.1
Consejería Economía, Innovación, Ciencia y Empleo, Junta de Andalucía FQM-229
Ministerio de Ciencia e Innovación de España MTM2011-28952-C02-01
European Regional Development Fund
The first and third authors were supported by the Russian Foundation for Basic Research (project no. 11-01-00330) and by a grant of the President of the Russian Federation (project no. NSh-4664.2012.1). The second author was supported by Junta de Andalucia (project nos. FQM-229 and P09-FQM-4643) and by Ministerio de Ciencia e Innovacion de Espana (project no. MTM2011-28952-C02-01) jointly with the European Regional Development Fund (ERDF).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 279, 25–51

Bibliographic databases:

UDC: 517.53
Received in April 2012

Citation: V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Method of interior variations and existence of $S$-compact sets”, Analytic and geometric issues of complex analysis, Collected papers, Trudy Mat. Inst. Steklova, 279, MAIK Nauka/Interperiodica, Moscow, 2012, 31–58; Proc. Steklov Inst. Math., 279 (2012), 25–51

Citation in format AMSBIB
\by V.~I.~Buslaev, A.~Mart{\'\i}nez-Finkelshtein, S.~P.~Suetin
\paper Method of interior variations and existence of $S$-compact sets
\inbook Analytic and geometric issues of complex analysis
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2012
\vol 279
\pages 31--58
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 279
\pages 25--51

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    This publication is cited in the following articles:
    1. V. I. Buslaev, “Convergence of multipoint Padé approximants of piecewise analytic functions”, Sb. Math., 204:2 (2013), 190–222  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. 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
    3. A. V. Komlov, S. P. Suetin, “An asymptotic formula for a two-point analogue of Jacobi polynomials”, Russian Math. Surveys, 68:4 (2013), 779–781  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. 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
    5. 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
    6. A. V. Komlov, S. P. Suetin, “Strong asymptotics of two-point Padé approximants for power-like multivalued functions”, Dokl. Math., 89:2 (2014), 165–168  mathnet  crossref  crossref  mathscinet  zmath  isi  isi  elib  elib  scopus
    7. V. I. Buslaev, S. P. Suetin, “An extremal problem in potential theory”, Russian Math. Surveys, 69:5 (2014), 915–917  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. V. I. Buslaev, “Convergence of $m$-point Padé approximants of a tuple of multivalued analytic functions”, Sb. Math., 206:2 (2015), 175–200  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. 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
    10. V. I. Buslaev, “Capacity of a compact set in a logarithmic potential field”, Proc. Steklov Inst. Math., 290:1 (2015), 238–255  mathnet  crossref  crossref  isi  elib  elib
    11. 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
    12. V. I. Buslaev, “An analogue of Polya's theorem for piecewise holomorphic functions”, Sb. Math., 206:12 (2015), 1707–1721  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    13. A. V. Komlov, N. G. Kruzhilin, R. V. Palvelev, S. P. Suetin, “Convergence of Shafer quadratic approximants”, Russian Math. Surveys, 71:2 (2016), 373–375  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. A. Martinez-Finkelshtein, E. .A. Rakhmanov, S. P. Suetin, “Asymptotics of Type I Hermite-Padé Polynomials for Semiclassical Functions”, Modern Trends in Constructive Function Theory, Conference and School on Constructive Functions in honor of Ed Saff's 70th Birthday Location (Vanderbilt Univ, Nashville, TN, 2014), Contemporary Mathematics, 661, 2016, 199–228  crossref  mathscinet  zmath  isi
    15. Buslaev V.I., Suetin S.P., “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  crossref  mathscinet  zmath  isi  elib  scopus
    16. 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
    17. S. P. Suetin, “On a new approach to the problem of distribution of zeros of Hermite–Padé polynomials for a Nikishin system”, Proc. Steklov Inst. Math., 301 (2018), 245–261  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    18. V. I. Buslaev, “On a lower bound for the rate of convergence of multipoint Padé approximants of piecewise analytic functions”, Izv. Math., 85:3 (2021), 351–366  mathnet  crossref  crossref  isi  elib
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