Approximation by polynomials and rational functions in weighted rearrangement invariant spaces

Let Γ be a Dini-smooth curve in the complex plane, and let G : = Int Γ . We prove some direct and inverse theorems of approximation theory by algebraic polynomials and rational functions in the weighted rearrangement invariant Smirnov spaces E X ( G , ω ) defined on G.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of mathematical analysis and applications Jg. 346; H. 2; S. 489 - 500
Hauptverfasser:	Israfilov, Daniyal M., Akgün, Ramazan
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	San Diego, CA Elsevier Inc 15.10.2008 Elsevier
Schlagworte:	Approximations and expansions Banach function spaces Constructive characterization Dini-smooth curve Direct theorems Exact sciences and technology Inverse theorems Mathematical analysis Mathematics Modulus of smoothness Real functions Sciences and techniques of general use Weighted rearrangement invariant space Inverse theorems Banach function spaces Weighted rearrangement invariant space Dini-smooth curve Constructive characterization Direct theorems Modulus of smoothness Polynomial function Polynomial Invariant Dini-smooth curve;Banach function spaces;Direct theorems;Inverse theorems;Weighted rearrangement invariant space;Modulus of smoothness;Constructive characterization Mathematical analysis Polynomial approximation Weight function Smooth function Approximation theory Application Rational function Direct theorem
ISSN:	0022-247X, 1096-0813
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Let Γ be a Dini-smooth curve in the complex plane, and let G : = Int Γ . We prove some direct and inverse theorems of approximation theory by algebraic polynomials and rational functions in the weighted rearrangement invariant Smirnov spaces E X ( G , ω ) defined on G.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2008.05.040