General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Mat. Sb.:

Personal entry:
Save password
Forgotten password?

Mat. Sb., 2015, Volume 206, Number 2, Pages 41–56 (Mi msb8347)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-12430
Ministry of Education and Science of the Russian Federation НШ-2900.2014.1


Full text: PDF file (552 kB)
References: PDF file   HTML file

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
\by M.~A.~Lapik
\paper Families of vector measures which are equilibrium measures in an external field
\jour Mat. Sb.
\yr 2015
\vol 206
\issue 2
\pages 41--56
\jour Sb. Math.
\yr 2015
\vol 206
\issue 2
\pages 211--224

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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. 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  crossref  mathscinet  zmath  isi
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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
    4. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. G. Lysov, “Silnaya asimptotika approksimatsii Ermita–Pade dlya sistemy Nikishina s vesami Yakobi”, Preprinty IPM im. M. V. Keldysha, 2017, 085, 35 pp.  mathnet  crossref
    6. 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  mathnet  crossref  crossref  isi  elib
    7. 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  mathnet  crossref  crossref  isi  elib
    8. 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
    9. 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
    10. 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  mathnet  crossref  crossref  isi  elib  elib
    11. 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.  mathnet  crossref  elib
    12. Lapik M.A., “Integral Formulas For Recovering Extremal Measures For Vector Constrained Energy Problems”, Lobachevskii J. Math., 40:9, SI (2019), 1355–1362  crossref  mathscinet  zmath  isi
    13. 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  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:429
    Full text:69
    First page:27

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021