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

This article is cited in 17 scientific papers (total in 17 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-229P09-FQM-4643 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, Tr. Mat. Inst. Steklova, 279, MAIK Nauka/Interperiodica, Moscow, 2012, 31–58; Proc. Steklov Inst. Math., 279 (2012), 25–51

Citation in format AMSBIB
\Bibitem{BusMarSue12} \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 Tr. Mat. Inst. Steklova \yr 2012 \vol 279 \pages 31--58 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3428} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3086756} \elib{http://elibrary.ru/item.asp?id=18447430} \transl \jour Proc. Steklov Inst. Math. \yr 2012 \vol 279 \pages 25--51 \crossref{https://doi.org/10.1134/S0081543812080044} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000314063000004} 

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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. V. I. Buslaev, “Convergence of multipoint Padé approximants of piecewise analytic functions”, Sb. Math., 204:2 (2013), 190–222
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
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
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
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
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
7. V. I. Buslaev, S. P. Suetin, “An extremal problem in potential theory”, Russian Math. Surveys, 69:5 (2014), 915–917
8. V. I. Buslaev, “Convergence of $m$-point Padé approximants of a tuple of multivalued analytic functions”, Sb. Math., 206:2 (2015), 175–200
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
10. V. I. Buslaev, “Capacity of a compact set in a logarithmic potential field”, Proc. Steklov Inst. Math., 290:1 (2015), 238–255
11. S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951
12. V. I. Buslaev, “An analogue of Polya's theorem for piecewise holomorphic functions”, Sb. Math., 206:12 (2015), 1707–1721
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
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
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
16. E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518
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
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