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Mat. Sb., 2006, Volume 197, Number 8, Pages 101–118 (Mi msb1480)  

This article is cited in 14 scientific papers (total in 14 papers)

Support of the extremal measure in a vector equilibrium problem

M. A. Lapik

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: A generalization of the Mhaskar–Saff functional is obtained for a vector equilibrium problem with an external field. As an application, the supports of the equilibrium measures are found in a special vector equilibrium problem with Nikishin matrix.
Bibliography: 13 titles.


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English version:
Sbornik: Mathematics, 2006, 197:8, 1205–1221

Bibliographic databases:

UDC: 517.53
MSC: 31A15
Received: 19.12.2005

Citation: M. A. Lapik, “Support of the extremal measure in a vector equilibrium problem”, Mat. Sb., 197:8 (2006), 101–118; Sb. Math., 197:8 (2006), 1205–1221

Citation in format AMSBIB
\by M.~A.~Lapik
\paper Support of the extremal measure in a vector equilibrium
\jour Mat. Sb.
\yr 2006
\vol 197
\issue 8
\pages 101--118
\jour Sb. Math.
\yr 2006
\vol 197
\issue 8
\pages 1205--1221

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    This publication is cited in the following articles:
    1. Balogh F., Bertola M., “Regularity of a vector potential problem and its spectral curve”, J. Approx. Theory, 161:1 (2009), 353–370  crossref  mathscinet  zmath  isi
    2. Beckermann B., Gryson A., “Extremal rational functions on symmetric discrete sets and superlinear convergence of the ADI method”, Constr. Approx., 32:3 (2010), 393–428  crossref  mathscinet  zmath  isi  elib
    3. A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov, “Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials”, Sb. Math., 202:2 (2011), 155–206  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Zhang L., Román P., “The asymptotic zero distribution of multiple orthogonal polynomials associated with Macdonald functions”, J. Approx. Theory, 163:2 (2011), 143–162  crossref  mathscinet  zmath  isi  elib
    5. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. M. A. Lapik, “Equilibrium measure for the vector logarithmic potential problem with an external field and the Nikishin interaction matrix”, Russian Math. Surveys, 67:3 (2012), 579–581  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Method of interior variations and existence of $S$-compact sets”, Proc. Steklov Inst. Math., 279 (2012), 25–51  mathnet  crossref  mathscinet  isi  elib
    8. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.  mathnet
    9. 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
    10. M. A. Lapik, “Formula Buyarova–Rakhmanova dlya vneshnego polya v vektornoi zadache ravnovesiya logarifmicheskogo potentsiala”, Preprinty IPM im. M. V. Keldysha, 2014, 082, 15 pp.  mathnet
    11. M. A. Lapik, “Families of vector measures which are equilibrium measures in an external field”, Sb. Math., 206:2 (2015), 211–224  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. M. A. Lapik, “Ekstremalnyi funktsional dlya vektornykh zadach ravnovesiya logarifmicheskogo potentsiala vo vneshnem pole s matritsei vzaimodeistviya Anzhelesko”, Preprinty IPM im. M. V. Keldysha, 2015, 083, 23 pp.  mathnet
    13. M. A. Lapik, “Ekstremalnaya mera i vneshnee pole v dvuparametricheskikh vektornykh zadachakh ravnovesiya logarifmicheskogo potentsiala”, Preprinty IPM im. M. V. Keldysha, 2016, 115, 20 pp.  mathnet  crossref
    14. Aptekarev A.I., “The Mhaskar–Saff Variational Principle and Location of the Shocks of Certain Hyperbolic Equations”, Modern Trends in Constructive Function Theory, Contemporary Mathematics, 661, ed. Hardin D. Lubinsky D. Simanek B., Amer Mathematical Soc, 2016, 167–186  crossref  mathscinet  zmath  isi
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