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Mat. Sb., 1993, Volume 184, Number 2, Pages 3–32 (Mi msb961)  

This article is cited in 22 scientific papers (total in 22 papers)

Rational approximation of analytic functions

V. A. Prokhorov

Belarusian State University

Abstract: This article is devoted to results relating to the theory of rational approximation of analytic functions. An analysis is made of the rate of decrease of the best approximations $\rho_n$ of an analytic functions of order at most $n$ in the uniform metric in terms connected with the properties of the function to be approximated, more precisely, connected with the distribution and structure of its set of singularities and with the character of its analytic continuation.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 78:1, 139–164

Bibliographic databases:

UDC: 517.53
MSC: Primary 30E10, 41A20; Secondary 41A50
Received: 10.10.1991 and 25.06.1992

Citation: V. A. Prokhorov, “Rational approximation of analytic functions”, Mat. Sb., 184:2 (1993), 3–32; Russian Acad. Sci. Sb. Math., 78:1 (1994), 139–164

Citation in format AMSBIB
\by V.~A.~Prokhorov
\paper Rational approximation of analytic functions
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 2
\pages 3--32
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 78
\issue 1
\pages 139--164

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    This publication is cited in the following articles:
    1. 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
    2. D.S Lubinsky, “On the diagonal Padé approximants of meromorphic functions”, Indagationes Mathematicae, 7:1 (1996), 97  crossref  mathscinet  zmath
    3. 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
    4. Prokhorov V., “Rates of Best Rational Approximation of Analytic Functions”, J. Approx. Theory, 107:2 (2000), 337–341  crossref  mathscinet  zmath  isi
    5. Prokhorov V. Saff E., “On Meromorphic Approximation”, Numer. Algorithms, 25:1-4 (2000), 305–321  crossref  mathscinet  zmath  adsnasa  isi
    6. Baratchart L. Stahl H. Wielonsky F., “Asymptotic Error Estimates for l-2 Best Rational Approximants to Markov Functions”, J. Approx. Theory, 108:1 (2001), 53–96  crossref  mathscinet  zmath  isi
    7. L. Baratchart, F. Seyfert, “An Lp Analog to AAK Theory for p⩾2”, Journal of Functional Analysis, 191:1 (2002), 52  crossref  mathscinet  zmath
    8. Prokhorov V., “On l-P-Generalization of a Theorem of Adamyan, Arov, and Krein”, J. Approx. Theory, 116:2 (2002), 380–396  crossref  mathscinet  zmath  isi
    9. Prokhorov V., “Rational Approximation of Analytic Functions Having Generalized Orders of Rate of Growth”, J. Comput. Anal. Appl., 5:1 (2003), 129–146  crossref  mathscinet  zmath  isi
    10. Prokhorov V., “On Best Rational Approximation of Analytic Functions”, J. Approx. Theory, 133:2 (2005), 284–296  crossref  mathscinet  zmath  isi
    11. 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
    12. Levin E. Saff E., “Potential Theoretic Tools in Polynomial and Rational Approximation”, Harmonic Analysis and Rational Approximation: their Roles in Signals, Control and Dynamical Systems, Lecture Notes in Control and Information Sciences, 327, Springer-Verlag Berlin, 2006, 71–94  crossref  mathscinet  zmath  isi
    13. Baratchart L., Yattselev M., “Convergent Interpolation to Cauchy Integrals Over Analytic Arcs”, Found. Comput. Math., 9:6 (2009), 675–715  crossref  mathscinet  zmath  isi
    14. Prokhorov V.A. Putinar M., “Compact Hankel Forms on Planar Domains”, Complex Anal. Oper. Theory, 3:2 (2009), 471–499  crossref  mathscinet  zmath  isi
    15. Kouchekian S. Prokhorov V.A., “On Estimates for the Ratio of Errors in Best Rational Approximation of Analytic Functions”, Trans. Am. Math. Soc., 361:5 (2009), 2649–2663  crossref  mathscinet  zmath  isi
    16. S. V. Rogosin, F.-O. Speck, “On the analytical solution of the linear-fractional Riemann problem”, Math. Nachr, 284:4 (2011), 543  crossref  mathscinet  zmath
    17. 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
    18. Baratchart L., Stahl H., Yattselev M., “Weighted extremal domains and best rational approximation”, Adv Math, 229:1 (2012), 357–407  crossref  mathscinet  zmath  isi
    19. Devendra Kumar, “On the Rational Approximation of Analytic Functions Having Generalized Types of Rate of Growth”, International Journal of Mathematics and Mathematical Sciences, 2012 (2012), 1  crossref  mathscinet
    20. Prokhorov V.A., “On Rational Approximation of Markov Functions on Finite Sets”, J. Approx. Theory, 191:SI (2015), 94–117  crossref  mathscinet  zmath  isi
    21. 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
    22. Yattselev M.L., “Symmetric Contours and Convergent Interpolation”, J. Approx. Theory, 225 (2018), 76–105  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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