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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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 346; no. 2; pp. 489 - 500
Main Authors: Israfilov, Daniyal M., Akgün, Ramazan
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 15.10.2008
Elsevier
Subjects:
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 Access:Get full text
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Description
Summary: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