Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 5

Approximation by p−Faber-Laurent rational functions in doubly-connected domain

Pages
1356–1366
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In this work, the approx-imation properties of the p−Faber-Laurent rational series expansions in the !−weightedSmirnov classes Ep(G, !) are studied.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let G be a doubly-connected domain bounded by regular curves.
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Key Findings & Data:Let G be a doubly-connected domain bounded by regular curves.
💡
Conclusion & Impact:In this work, the approx-imation properties of the p−Faber-Laurent rational series expansions in the !−weightedSmirnov classes Ep(G, !) are studied.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Let G be a doubly-connected domain bounded by regular curves. In this work, the approx-imation properties of the p−Faber-Laurent rational series expansions in the !−weightedSmirnov classes Ep(G, !) are studied.

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Cite This Article

Jafarov, S. Z. (2022). Approximation by p−Faber-Laurent rational functions in doubly-connected domain. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 5, 1356–1366. https://ajindex.com/articles/530136

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References (15)

  1. S.Y. Alper, Approximation in the mean of analytic functions of class Ep (in Russian), in: Investigations on the Modern Problems of the Function Theory of a Complex Variable, Gos. Izdat. Fiz.-Mat. 272-2386, Lit. Moscow, 1960
  2. J.E. Andersson, On the degree of polynomial approximation in Ep(D), J. Approx. Theory 19, 61-68, 1977
  3. A. Cavus and D.M. Israfilov, Approximation by Faber-Laurent retional functions in the mean of functions of the class Lp(􀀀) with 1 [4] P.L. Duren, Theory of Hp spaces, Academic Press, 1970
  4. E.M. Dyn’kin, The rate of polynomial approximation in complex domain, in: Complex Analysis and Spectral Theory, 90-142, Springer-Verlag, Berlin, 1980
  5. E.M. Dyn’kin and B.P. Osilenker, Weighted estimates for singular integrals and their appllications, in: Mathematical Analysis 21., 42-129, Akad. Nauk. SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1983
  6. G.M. Goluzin, Geometric Theory of Functions of a Complex Variable, Translation of Mathematical Monographs 26, Providence, RI: AMS, 1968
  7. A. Guven and D.M. Israfilov, Approximation in rearrangement invariant spaces on Carleson curves, East J. Approx. 12 (4), 381-395, 2006
  8. A. Guven and D.M. Israfilov, Improved inverse theorems in weighted Lebesgue and Smirnov spaces, Bul. Belg. Math. Soc. Simon Stevin 14, 681-692, 2007
  9. E.A. Haciyeva, Investigation of the properties of functions with quasimonotone Fourier coefficients in generalized Nikolsky- Besov spaces, Author’s summary of can- didates dissertation, Tbilisi, (In Russian)
  10. I.I. Ibragimov and J.I. Mamedkanov, A constructive characterization of a certain class of functions, Dokl. Akad. Nauk SSSR 223, 35-37, 1975, Soviet Math. Dokl. 4, 820-823, 1976
  11. D.M. Israfilov, Approximate properties of the generalized Faber series in an integral metric (in Russian), Izv. Akad. Nauk Az. SSR, Fiz.-Tekh. Math. Nauk 2, 10-14, 1987
  12. D.M. Israfilov, Approximation by p-Faber polynomials in the weighted Smirnov class Ep(G,w) and the Bieberbach polynomials, Constr. Approx. 17, 335-351, 2001
  13. D.M. Israfilov, Approximation by p−Faber-Laurent rational functions in weighted Lebesgue spaces, Chechoslovak Math. J. 54, 751-765, 2004
  14. D.M. Israfilov and R. Akgün, Approximation by polynomials and rational functions in weighted rearrangement invariant spaces, J. Math.Anal. Appl. 346, 489-500, 2008
  15. D.M. Israfilov and A. Guven, Approximation in weighted Smirnov classes, East J. Approx. 11 (1), 91-102, 2005. [