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This article is cited in 13 scientific papers (total in 13 papers)
Families of vector measures which are equilibrium measures in an external field
M. A. Lapik
M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow
Abstract:
We consider vector extremal problems in the theory of logarithmic potential with external field by looking at an example of two-dimensional problems with Nikishin interaction matrix and variable masses $2x$ and $x$ of the first and second components of the vector measure, respectively. The dependence of the supports of the equilibrium measures, equlibrium constants and energy on the parameter $x$ is analysed. Integral formulae recovering the
extremal measure with mass $x$ from the supports of extremal measures with smaller masses are obtained.
Bibliography: 27 titles.
Keywords:
logarithmic vector potential, extremal vector measure.
DOI:
https://doi.org/10.4213/sm8347
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English version:
Sbornik: Mathematics, 2015, 206:2, 211–224
Bibliographic databases:
     
UDC:
517.53
MSC: 31A10, 31A15
Received: 17.02.2014 and 08.12.2014
Citation:
M. A. Lapik, “Families of vector measures which are equilibrium measures in an external field”, Mat. Sb., 206:2 (2015), 41–56; Sb. Math., 206:2 (2015), 211–224
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/msb8347https://doi.org/10.4213/sm8347 http://mi.mathnet.ru/eng/msb/v206/i2/p41
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A. I. Aptekarev, “The Mhaskar-Saff variational principle and location of the shocks of certain hyperbolic equations”, Moder trends in constructive function theory, Conference and School on Constructive Functions in honor of Ed Saff's 70th Birthday (Vanderbilt Univ, Nashville, 2014), Contemp. Math., 661, Amer. Math. Soc., Providence, RI, 2016, 167–186
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S. P. Suetin, “Zero distribution of Hermite–Padé polynomials and localization of branch points of multivalued analytic functions”, Russian Math. Surveys, 71:5 (2016), 976–978
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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.
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S. P. Suetin, “An Analog of Pólya's Theorem for Multivalued Analytic Functions with Finitely Many Branch Points”, Math. Notes, 101:5 (2017), 888–898
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V. G. Lysov, “Silnaya asimptotika approksimatsii Ermita–Pade dlya sistemy Nikishina s vesami Yakobi”, Preprinty IPM im. M. V. Keldysha, 2017, 085, 35 pp.
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V. G. Lysov, D. N. Tulyakov, “On a Vector Potential-Theory Equilibrium Problem with the Angelesco Matrix”, Proc. Steklov Inst. Math., 298 (2017), 170–200
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A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Proc. Steklov Inst. Math., 298 (2017), 317–333
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E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518
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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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V. G. Lysov, D. N. Tulyakov, “On the supports of vector equilibrium measures in the Angelesco problem with nested intervals”, Proc. Steklov Inst. Math., 301 (2018), 180–196
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M. A. Lapik, “Formuly vosstanovleniya ravnovesnykh mer dlya zadach ravnovesiya vektornogo potentsiala s ogranicheniyami na mery i vneshnimi polyami”, Preprinty IPM im. M. V. Keldysha, 2018, 203, 16 pp.
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Lapik M.A., “Integral Formulas For Recovering Extremal Measures For Vector Constrained Energy Problems”, Lobachevskii J. Math., 40:9, SI (2019), 1355–1362
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Aptekarev A.I. Lapik M.A. Lysov V.G., “Direct and Inverse Problems For Vector Logarithmic Potentials With External Fields”, Anal. Math. Phys., 9:3 (2019), 919–935
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