Some Theorems of Approximation Theory in Weighted Smirnov Classes with Variable Exponent

Let G ⊂ C be a Jordan domain with rectifiable Dini smooth boundary Γ . In this work, we investigate approximation properties of matrix transforms constructed via Faber series in weighted Smirnov classes with variable exponent. Moreover, direct and inverse theorems of approximation theory in weighted...

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Bibliographic Details
Published in:Computational methods and function theory Vol. 20; no. 1; pp. 39 - 61
Main Author: Testici, Ahmet
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020
Springer Nature B.V
Subjects:
Analysis
Approximation
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematical analysis
Mathematics
Mathematics and Statistics
Smooth boundaries
Theorems
30E10
Matrix transforms
Direct and inverse theorems
Faber series
Faber operators
41A30
41A10
Muckenhoupt weights
Weighted variable exponent Smirnov classes
ISSN:1617-9447, 2195-3724
Online Access:Get full text
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Summary:Let G ⊂ C be a Jordan domain with rectifiable Dini smooth boundary Γ . In this work, we investigate approximation properties of matrix transforms constructed via Faber series in weighted Smirnov classes with variable exponent. Moreover, direct and inverse theorems of approximation theory in weighted Smirnov classes with variable exponent are proved and some results related to constructive characterization in generalized Lipschitz classes are obtained.
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ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-019-00296-7