RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1987, Volume 134(176), Number 3(11), Pages 306–352 (Mi msb2759)  

This article is cited in 111 scientific papers (total in 113 papers)

Equilibrium distributions and degree of rational approximation of analytic functions

A. A. Gonchar, E. A. Rakhmanov


Abstract: A theorem is proved on the degree of rational approximation of sequences of analytic functions given by Cauchy-type integrals of the form
$$ f_n(z)=\oint_F\Phi_n(t)f(t)(t-z)^{-1} dt,\qquad z\in E. $$
The theorem is formulated in terms connected with the equilibrium distribution of the charge on the plates of a capacitor $(E,F)$ under the assumption that an external field $\varphi=\lim_{n\to\infty}(2n)^{-1}\log|\Phi_n|^{-1}$ acts on the plate $F$, and this plate satisfies a certain symmetry condition in the field $\varphi$. The theorem is used to solve the problem of the degree of rational approximation of the function $e^{-x}$ on $[0,+\infty)$.
Bibliography: 44 titles.

Full text: PDF file (2487 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1989, 62:2, 305–348

Bibliographic databases:

UDC: 517.53
MSC: Primary 41A20, 41A25, 31A15; Secondary 41A21, 30C15, 33A65, 33A25
Received: 18.04.1987

Citation: A. A. Gonchar, E. A. Rakhmanov, “Equilibrium distributions and degree of rational approximation of analytic functions”, Mat. Sb. (N.S.), 134(176):3(11) (1987), 306–352; Math. USSR-Sb., 62:2 (1989), 305–348

Citation in format AMSBIB
\Bibitem{GonRak87}
\by A.~A.~Gonchar, E.~A.~Rakhmanov
\paper Equilibrium distributions and degree of rational approximation of
analytic functions
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 134(176)
\issue 3(11)
\pages 306--352
\mathnet{http://mi.mathnet.ru/msb2759}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=922628}
\zmath{https://zbmath.org/?q=an:0663.30039|0645.30026}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 62
\issue 2
\pages 305--348
\crossref{https://doi.org/10.1070/SM1989v062n02ABEH003242}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987U023000002}


Linking options:
  • http://mi.mathnet.ru/eng/msb2759
  • http://mi.mathnet.ru/eng/msb/v176/i3/p306

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. D. S. Lubinsky, “Distribution of poles of diagonal rational approximants to functions of fast rational approximability”, Constr Approx, 7:1 (1991), 501  crossref  mathscinet  zmath  isi
    2. R. S. Varga, A. Ruttan, A. J. Carpenter, “Numerical results on best uniform rational approximation of $|x|$ on $[-1,1]$”, Math. USSR-Sb., 74:2 (1993), 271–290  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Finkelshtein A., “Rational Approximation Rate of Exp(-X) Function on Positive Semians”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1991, no. 6, 94–96  isi
    4. Varga R., “How High-Precision Calculations Can Stimulate Mathematical Research”, Appl. Numer. Math., 10:3-4 (1992), 177–193  crossref  mathscinet  zmath  isi
    5. Prokhorov V., “On Approximation of Analytic-Functions by Rational Functions”, Dokl. Akad. Nauk, 327:4-6 (1992), 438–441  mathnet  mathscinet  zmath  isi
    6. V. A. Prokhorov, “Rational approximation of analytic functions”, Russian Acad. Sci. Sb. Math., 78:1 (1994), 139–164  mathnet  crossref  mathscinet  zmath  isi
    7. V. A. Prokhorov, “On the degree of rational approximation of meromorphic functions”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 1–20  mathnet  crossref  mathscinet  zmath  isi
    8. Prokhorov V., “On the Best Rational Approximation of Analytic-Functions”, Dokl. Akad. Nauk Belarusi, 38:2 (1994), 19–22  mathscinet  zmath  isi
    9. A. P. Starovoitov, N. A. Starovoitova, “Asymptotic behaviour of the Hadamard determinants and the behaviour of the rows of the Padé and Chebyshev tables for a sum of exponentials”, Sb. Math., 187:2 (1996), 297–313  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Amos J. Carpenter, “Scientific computation on some mathematical problems”, Journal of Computational and Applied Mathematics, 66:1-2 (1996), 111  crossref
    11. Gonzalez J., “Asymptotics for Angelesco-Nikishin Systems”, J. Approx. Theory, 85:1 (1996), 43–68  crossref  mathscinet  zmath  isi
    12. A. A. Gonchar, E. A. Rakhmanov, V. N. Sorokin, “Hermite–Pade approximants for systems of Markov-type functions”, Sb. Math., 188:5 (1997), 671–696  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. A. Bultheel, C. Díaz-Mendoza, P. González-Vera, R. Orive, “Quadrature on the half-line and two-point Padé approximants to Stieltjes functions—II: Convergence”, Journal of Computational and Applied Mathematics, 77:1-2 (1997), 53  crossref
    14. Herbert Stahl, “The convergence of diagonal Padé approximants and the Padé Conjecture”, Journal of Computational and Applied Mathematics, 86:1 (1997), 287  crossref
    15. Suetin S., “On the Asymptotics of Denominators of Pade' Approximants to Orthogonal Expansions”, Dokl. Akad. Nauk, 356:6 (1997), 744–746  mathnet  mathscinet  zmath  isi
    16. Tulyakov D., “On Exact Rational Approximations Rate of E(-X) on [0;+Infinity) by Inverse Taylor Sums”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1997, no. 2, 9–14  mathscinet  zmath  isi
    17. Herbert Stahl, “Spurious poles in Padé approximation”, Journal of Computational and Applied Mathematics, 99:1-2 (1998), 511  crossref
    18. Ya Yan Lu, “Exponentials of symmetric matrices through tridiagonal reductions”, Linear Algebra and its Applications, 279:1-3 (1998), 317  crossref
    19. Prokhorov V. Staff E., “Rates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions”, Constr. Approx., 15:2 (1999), 155–173  crossref  mathscinet  zmath  isi
    20. Andrei Martı́nez-Finkelshtein, Pedro Martı́nez-González, Ramón Orive, “On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters”, Journal of Computational and Applied Mathematics, 133:1-2 (2001), 477  crossref
    21. Baratchart L. Stahl H. Wielonsky F., “Asymptotic Uniqueness of Best Rational Approximants of Given Degree to Markov Functions in l-2 of the Circle”, Constr. Approx., 17:1 (2001), 103–138  crossref  mathscinet  zmath  isi
    22. S. P. Suetin, “Padé approximants and efficient analytic continuation of a power series”, Russian Math. Surveys, 57:1 (2002), 43–141  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. A. A. Bolibrukh, A. G. Vitushkin, V. S. Vladimirov, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, A. G. Sergeev, P. L. Ul'yanov, L. D. Faddeev, E. M. Chirka, “Andrei Aleksandrovich Gonchar (on his 70th birthday)”, Russian Math. Surveys, 57:1 (2002), 191–198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    24. V. N. Sorokin, “Cyclic graphs and Apéry's theorem”, Russian Math. Surveys, 57:3 (2002), 535–571  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Sb. Math., 193:1 (2002), 1–72  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    26. Baratchart L., Seyfert F., “An l-P Analog to Aak Theory for P >= 2”, J. Funct. Anal., 191:1 (2002), 52–122  crossref  mathscinet  zmath  isi
    27. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57  mathnet  crossref  crossref  mathscinet  zmath  isi
    28. Hernandez M. Ceniceros J., “Strong Asymptotic Behavior for Extremal Polynomials with Respect to Varying Measures on the Unit Circle”, J. Approx. Theory, 125:1 (2003), 131–144  crossref  mathscinet  zmath  isi
    29. A. B. J. Kuijlaars, A. Martínez-Finkelshtein, “Strong asymptotics for Jacobi polynomials with varying nonstandard parameters”, J Anal Math, 94:1 (2004), 195  crossref  mathscinet  zmath  isi  elib
    30. Spyridon Kamvissis, Evguenii A. Rakhmanov, “Existence and regularity for an energy maximization problem in two dimensions”, J Math Phys (N Y ), 46:8 (2005), 083505  crossref  mathscinet  zmath  isi
    31. R. F. Khabibullin, “Asymptotic Series for Bessel Polynomials”, Math. Notes, 77:6 (2005), 878–881  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    32. A. Martínez-Finkelshtein, R. Orive, “Riemann–Hilbert analysis for Jacobi polynomials orthogonal on a single contour”, Journal of Approximation Theory, 134:2 (2005), 137  crossref
    33. Trefethen, LN, “Talbot quadratures and rational approximations”, BIT Numerical Mathematics, 46:3 (2006), 653  crossref  isi  elib
    34. Baratchart L., “A Remark on Uniqueness of Best Rational Approximants of Degree 1 in l-2 of the Circle”, Electron. Trans. Numer. Anal., 25 (2006), 54–66  mathscinet  zmath  isi
    35. Thomas Schmelzer, Lloyd N. Trefethen, “Computing the Gamma Function Using Contour Integrals and Rational Approximations”, SIAM J Numer Anal, 45:2 (2007), 558  crossref  mathscinet  zmath  isi  elib
    36. A. P. Starovoitov, N. A. Starovoitova, “Padé approximants of the Mittag-Leffler functions”, Sb. Math., 198:7 (2007), 1011–1023  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    37. Schmelzer T., Trefethen L.N., “Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals”, Electron. Trans. Numer. Anal., 29 (2007), 1–18  mathscinet  isi
    38. A. A. Kandayan, “Multipoint Padé Approximations of the Beta Function”, Math. Notes, 85:2 (2009), 176–189  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    39. S. P. Suetin, “Strong asymptotics of polynomials orthogonal with respect to a complex weight”, Sb. Math., 200:1 (2009), 77–93  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    40. V. N. Sorokin, “Generalized Pollaczek polynomials”, Sb. Math., 200:4 (2009), 577–595  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    41. Yu. A. Labych, A. P. Starovoitov, “Trigonometric Padé approximants for functions with regularly decreasing Fourier coefficients”, Sb. Math., 200:7 (2009), 1051–1074  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    42. L. Baratchart, M. L. Yattselev, “Meromorphic approximants to complex Cauchy transforms with polar singularities”, Sb. Math., 200:9 (2009), 1261–1297  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    43. Alphonse P. Magnus, “Elliptic Hypergeometric Solutions to Elliptic Difference Equations”, SIGMA, 5 (2009), 038, 12 pp.  mathnet  crossref  mathscinet  zmath
    44. Baratchart, L, “Convergent Interpolation to Cauchy Integrals over Analytic Arcs”, Foundations of Computational Mathematics, 9:6 (2009), 675  crossref  isi  elib
    45. Stahl, H, “An extension of the '1/9'-problem”, Journal of Computational and Applied Mathematics, 233:3 (2009), 821  crossref  isi
    46. Baratchart, L, “Multipoint Pade approximants to complex Cauchy transforms with polar singularities”, Journal of Approximation Theory, 156:2 (2009), 187  crossref  isi
    47. Deano A., Huybrechs D., Kuijlaars A.B.J., “Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature”, Journal of Approximation Theory, 162:12 (2010), 2202–2224  crossref  isi
    48. Baratchart L., Yattselev M., “Convergent Interpolation to Cauchy Integrals over Analytic Arcs with Jacobi-Type Weights”, International Mathematics Research Notices, 2010, no. 22, 4211–4275  isi
    49. Stahl H., “A Potential-Theoretic Problem Connected with Complex Orthogonality”, Recent Trends in Orthogonal Polynomials and Approximation Theory, Contemporary Mathematics, 507, 2010, 255–285  crossref  isi
    50. Marcellan F., Martinez-Finkelshtein A., “Guillermo Lopez Lagomasino: Mathematical Life”, Recent Trends in Orthogonal Polynomials and Approximation Theory, Contemporary Mathematics, 507, eds. Arvesu J., Marcellan F., MartinezFinkelshtein A., Amer Mathematical Soc, 2010, 1–24  crossref  mathscinet  zmath  isi
    51. Martinez-Finkelshtein A., Rakhmanov E.A., “On Asymptotic Behavior of Heine-Stieltjes and Van Vleck Polynomials”, Recent Trends in Orthogonal Polynomials and Approximation Theory, Contemporary Mathematics, 507, eds. Arvesu J., Marcellan F., MartinezFinkelshtein A., Amer Mathematical Soc, 2010, 209–232  crossref  mathscinet  zmath  isi
    52. E. A. Rakhmanov, “The asymptotics of Hermite-Padé polynomials for two Markov-type functions”, Sb. Math., 202:1 (2011), 127–134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    53. A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, “Variation of the equilibrium measure and the $S$-property of a stationary compact set”, Russian Math. Surveys, 66:1 (2011), 176–178  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    54. C. Díaz Mendoza, R. Orive, “The Szegő curve and Laguerre polynomials with large negative parameters”, Journal of Mathematical Analysis and Applications, 379:1 (2011), 305  crossref
    55. A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, “Variation of the equilibrium energy and the $S$-property of stationary compact sets”, Sb. Math., 202:12 (2011), 1831–1852  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    56. 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
    57. A. I. Aptekarev, G. López Lagomasino, E. B. Saff, V. Totik, H. Stahl, “Andrei Aleksandrovich Gonchar (on his 80th birthday)”, Russian Math. Surveys, 66:6 (2011), 1209–1216  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    58. A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    59. Martinez-Finkelshtein A., Rakhmanov E.A., “Critical Measures, Quadratic Differentials, and Weak Limits of Zeros of Stieltjes Polynomials”, Comm Math Phys, 302:1 (2011), 53–111  crossref  isi
    60. Fidalgo Prieto U., Lopez Lagomasino G., “Nikishin Systems Are Perfect”, Constr Approx, 34:3 (2011), 297–356  crossref  isi
    61. Rakhmanov E.A., “Orthogonal Polynomials and S-Curves”, Recent Advances in Orthogonal Polynomials, Special Functions, and their Applications, Contemporary Mathematics, 578, ed. Arvesu J. Lagomasino G., Amer Mathematical Soc, 2011, 195–239  crossref  isi
    62. Yu. A. Labych, A. P. Starovoitov, “Priblizhenie nepreryvnykh funktsii ratsionalnymi drobyami Pade–Chebysheva”, PFMT, 2011, no. 1(6), 69–78  mathnet
    63. Martinez-Finkelshtein A., Rakhmanov E.A., Suetin S.P., “Heine, Hilbert, Pade, Riemann, and Stieltjes: John Nuttall's Work 25 Years Later”, Recent Advances in Orthogonal Polynomials, Special Functions, and their Applications, Contemporary Mathematics, 578, eds. Arvesu J., Lagomasino G., Amer Mathematical Soc, 2011, 165–193  crossref  mathscinet  isi
    64. A. V. Komlov, S. P. Suetin, “Widom's formula for the leading coefficient of a polynomial which is orthonormal with respect to a varying weight”, Russian Math. Surveys, 67:1 (2012), 183–185  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    65. Baratchart L., Stahl H., Yattselev M., “Weighted extremal domains and best rational approximation”, Adv Math, 229:1 (2012), 357–407  crossref  isi
    66. E. A. Rakhmanov, S. P. Suetin, “Asymptotic behaviour of the Hermite–Padé polynomials of the 1st kind for a pair of functions forming a Nikishin system”, Russian Math. Surveys, 67:5 (2012), 954–956  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    67. A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of Meixner polynomials and Christoffel-Darboux kernels”, Trans. Moscow Math. Soc., 73 (2012), 67–106  mathnet  crossref  mathscinet  zmath  elib
    68. A. V. Komlov, S. P. Suetin, “An asymptotic formula for polynomials orthonormal with respect to a varying weight”, Trans. Moscow Math. Soc., 73 (2012), 139–159  mathnet  crossref  mathscinet  zmath  elib
    69. 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
    70. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.  mathnet
    71. 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
    72. T. Claeys, F. Wielonsky, “On sequences of rational interpolants of the exponential function with unbounded interpolation points”, Journal of Approximation Theory, 171 (2013), 1  crossref
    73. Lukashov A., Akal C., “Determinant Form and a Test of Convergence for the Newton-Pade Approximations”, J. Comput. Anal. Appl., 15:1 (2013), 55–64  zmath  isi
    74. Gabriel Álvarez, L.M.artínez Alonso, Elena Medina, “Determination ofS-curves with applications to the theory of non-Hermitian orthogonal polynomials”, J. Stat. Mech, 2013:06 (2013), P06006  crossref
    75. Boris Konopelchenko, L.M.artínez Alonso, Elena Medina, “Spectral curves in gauge/string dualities: integrability, singular sectors and regularization”, J. Phys. A: Math. Theor, 46:22 (2013), 225203  crossref
    76. Vilmos Totik, “A Note on Rational
      $$L^p$$
      L p Approximation on Jordan Curves”, Comput. Methods Funct. Theory, 2013  crossref
    77. K. Jordaan, F. Toókos, “Orthogonality and asymptotics of Pseudo-Jacobi polynomials for non-classical parameters”, Journal of Approximation Theory, 2013  crossref
    78. 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
    79. 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
    80. M.J. Atia, A. Martínez-Finkelshtein, P. Martínez-González, F. Thabet, “Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters”, Journal of Mathematical Analysis and Applications, 2014  crossref
    81. 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
    82. Daan Huybrechs, A.B..J. Kuijlaars, Nele Lejon, “Zero distribution of complex orthogonal polynomials with respect to exponential weights”, Journal of Approximation Theory, 2014  crossref
    83. Alfredo Deaño, “Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval”, Journal of Approximation Theory, 186 (2014), 33  crossref
    84. L.N.. Trefethen, J. A. C. Weideman, “The Exponentially Convergent Trapezoidal Rule”, SIAM Rev, 56:3 (2014), 385  crossref
    85. 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
    86. Gabriel Álvarez, Luis Martínez Alonso, Elena Medina, “Phase structure and asymptotic zero densities of orthogonal polynomials in the cubic model”, Journal of Computational and Applied Mathematics, 2014  crossref
    87. 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
    88. 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
    89. 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
    90. Kuijlaars A.B.J. Silva G.L.F., “S-Curves in Polynomial External Fields”, J. Approx. Theory, 191:SI (2015), 1–37  crossref  isi
    91. Gabriel Álvarez, L.M.artínez Alonso, Elena Medina, “Fine structure in the large <mml:math altimg="si19.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>n</mml:mi></mml:math> limit of the non-Hermitian Penner matrix model”, Annals of Physics, 2015  crossref
    92. 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
    93. 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
    94. 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
    95. 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
    96. A. V. Komlov, S. P. Suetin, “Distribution of the zeros of Hermite–Padé polynomials”, Russian Math. Surveys, 70:6 (2015), 1179–1181  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    97. Martinez-Finkelshtein A., Orive R., Rakhmanov E.A., “Phase Transitions and Equilibrium Measures in Random Matrix Models”, Commun. Math. Phys., 333:3 (2015), 1109–1173  crossref  mathscinet  zmath  isi  elib
    98. Aptekarev A.I. Yattselev M.L., “Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials”, Acta Math., 215:2 (2015), 217–280  crossref  mathscinet  zmath  isi  scopus
    99. E. A. Rakhmanov, “The Gonchar-Stahl $\rho^2$-theorem and associated directions in the theory of rational approximations of analytic functions”, Sb. Math., 207:9 (2016), 1236–1266  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    100. V. I. Buslaev, “The Capacity of the Rational Preimage of a Compact Set”, Math. Notes, 100:6 (2016), 781–790  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    101. 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  scopus
    102. 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  zmath  isi
    103. Martinez-Finkelshtein A. Rakhmanov E.A. Suetin S.P., “Asymptotics of Type I Hermite–Padé Polynomials for Semiclassical Functions”, Modern Trends in Constructive Function Theory, Contemporary Mathematics, 661, ed. Hardin D. Lubinsky D. Simanek B., Amer Mathematical Soc, 2016, 199–228  crossref  zmath  isi
    104. Alvarez G. Martinez Alonso L. Medina E., “Complex saddle points in the Gross-Witten-Wadia matrix model”, Phys. Rev. D, 94:10 (2016), 105010  crossref  isi  elib  scopus
    105. A. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka, “Hermite–Padé approximants for meromorphic functions on a compact Riemann surface”, Russian Math. Surveys, 72:4 (2017), 671–706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    106. V. I. Buslaev, “On the Van Vleck Theorem for Limit-Periodic Continued Fractions of General Form”, Proc. Steklov Inst. Math., 298 (2017), 68–93  mathnet  crossref  crossref  mathscinet  isi  elib
    107. 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
    108. V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    109. Yattselev M.L., “Symmetric Contours and Convergent Interpolation”, J. Approx. Theory, 225 (2018), 76–105  crossref  isi
    110. V. I. Buslaev, “On Singular points of Meromorphic Functions Determined by Continued Fractions”, Math. Notes, 103:4 (2018), 527–536  mathnet  crossref  crossref  mathscinet  isi  elib
    111. 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
    112. 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
    113. E. M. Chirka, “Potentials on a compact Riemann surface”, Proc. Steklov Inst. Math., 301 (2018), 272–303  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:1246
    Full text:304
    References:52
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020