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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 5

APPROXIMATION BY INTERPOLATING POLYNOMIALS IN WEIGHTED SYMMETRIC SMIRNOV SPACES

Ramazan AKGÜN
Hüseyin KOÇ
Sayfa
643–649
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

It is proved that the convergence rate of complex interpolating polynomials and the convergence rate of best approximating algebraic polynomials are the same in the norm of Symmetric Smirnov Spaces.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let Γ ⊂ C be a closed BR curve without cusps.
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Temel Bulgular & Veri:In this work approximation by complex interpolating polynomials in a Weighted Symmetric Smirnov Space is studied.
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Sonuç & Katkı:It is proved that the convergence rate of complex interpolating polynomials and the convergence rate of best approximating algebraic polynomials are the same in the norm of Symmetric Smirnov Spaces.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Curve of bounded rotation · Faber polynomials · Interpolating polynomial

Abstract

Let Γ ⊂ C be a closed BR curve without cusps. In this work approximation by complex interpolating polynomials in a Weighted Symmetric Smirnov Space is studied. It is proved that the convergence rate of complex interpolating polynomials and the convergence rate of best approximating algebraic polynomials are the same in the norm of Symmetric Smirnov Spaces.

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Bu Makaleye Atıf Yap

AKGÜN, R., KOÇ, H. (2022). APPROXIMATION BY INTERPOLATING POLYNOMIALS IN WEIGHTED SYMMETRIC SMIRNOV SPACES. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 5, 643–649. https://ajindex.com/articles/530489

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Kaynakça (11)

  1. Akg¨un, R. and Israfilov, D. M. Approximation by interpolating polynomials in Smirnov- Orlicz class, J. Korean Math. Soc. 43, 412–424, 2006.
  2. Benneth, C. and Sharpley, R. Interpolation of operators (Pure and Applied Mathematics 129, Academic Press, Boston, 1988).
  3. Boyd, D. W. Spaces between a pair of reflexive Lebesgue spaces, Proc. Amer. Math. Soc. 18, 215–219, 1967.
  4. Gaier, D. Lectures on complex approximation (Birkh¨auser, Boston, Basel, Stuttgart, 1987). [5] Garnett, J. B. Bounded analytic functions (Pure and Applied Mathematics 96, Academic Press Inc. [Harcourt Brace Jovanovich, Publishers], New York, London, 1981). [6] Karlovich, A. Yu. Algebras of singular integral operators with PC coefficients in rearrangement-invariant spaces with Muckenhoupt weights, J. Operator Theory 47, 303– 323, 2002. H. Ko¸c, Convergence of interpolating polynomials in symmetric function spaces (M.Sci. Thesis, Balikesir University, Institute of Science, 2011).
  5. Pommerenke, Ch. Conforme abbildung und Fekete-punkte, Mathematische Zeitschrift 89, 422–438, 1965.
  6. Pommerenke, Ch. Boundary behaviour of conformal maps (Grundlehren der Mathema- tischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 299, Springer- Verlag, Berlin, 1992).
  7. Shen, X. C. and Zhong, L. On Lagrange interpolation in Ep(D) for 1 Smirnov, V. I. and Lebedev, N. A. Functions of complex variable: Constructive theory (The M. I. T. Press,
  8. Cambridge, Mass., 1968).
  9. Suetin, P. K. Series of Faber Polynomials (Gordon and Breach, 1 Reading, 1998).
  10. Zhong, L. and Zhu, L. Convergence of the interpolants based on the roots of Faber polyno- mials, Acta Math. Hungarica 65 (3), 273–283, 1994.
  11. Zhu, L. Y. A new class of interpolation nodes, (in Chinese) Advances in Mathematics 24 (4), 327-ˆu334, 1995.