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

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

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
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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. V. A. Prokhorov, “On the degree of rational approximation of meromorphic functions”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 1–20
2. D.S Lubinsky, “On the diagonal Padé approximants of meromorphic functions”, Indagationes Mathematicae, 7:1 (1996), 97
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
4. Prokhorov V., “Rates of Best Rational Approximation of Analytic Functions”, J. Approx. Theory, 107:2 (2000), 337–341
5. Prokhorov V. Saff E., “On Meromorphic Approximation”, Numer. Algorithms, 25:1-4 (2000), 305–321
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
7. L. Baratchart, F. Seyfert, “An Lp Analog to AAK Theory for p⩾2”, Journal of Functional Analysis, 191:1 (2002), 52
8. Prokhorov V., “On l-P-Generalization of a Theorem of Adamyan, Arov, and Krein”, J. Approx. Theory, 116:2 (2002), 380–396
9. Prokhorov V., “Rational Approximation of Analytic Functions Having Generalized Orders of Rate of Growth”, J. Comput. Anal. Appl., 5:1 (2003), 129–146
10. Prokhorov V., “On Best Rational Approximation of Analytic Functions”, J. Approx. Theory, 133:2 (2005), 284–296
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
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
13. Baratchart L., Yattselev M., “Convergent Interpolation to Cauchy Integrals Over Analytic Arcs”, Found. Comput. Math., 9:6 (2009), 675–715
14. Prokhorov V.A. Putinar M., “Compact Hankel Forms on Planar Domains”, Complex Anal. Oper. Theory, 3:2 (2009), 471–499
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
16. S. V. Rogosin, F.-O. Speck, “On the analytical solution of the linear-fractional Riemann problem”, Math. Nachr, 284:4 (2011), 543
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
18. Baratchart L., Stahl H., Yattselev M., “Weighted extremal domains and best rational approximation”, Adv Math, 229:1 (2012), 357–407
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
20. Prokhorov V.A., “On Rational Approximation of Markov Functions on Finite Sets”, J. Approx. Theory, 191:SI (2015), 94–117
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
22. Yattselev M.L., “Symmetric Contours and Convergent Interpolation”, J. Approx. Theory, 225 (2018), 76–105
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