Inverse Jackson theorems in spaces with integral metric

In the spaces L ψ ( T ) of periodic functions with metric where ψ is a function of the modulus-of-continuity type, we investigate the inverse Jackson theorems in the case of approximation by trigonometric polynomials. It is proved that an inverse Jackson theorem is true if and only if the lower dila...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2012-08, Vol.64 (3), p.394-407
Main Author: Pichugov, S. A.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Summary:In the spaces L ψ ( T ) of periodic functions with metric where ψ is a function of the modulus-of-continuity type, we investigate the inverse Jackson theorems in the case of approximation by trigonometric polynomials. It is proved that an inverse Jackson theorem is true if and only if the lower dilation exponent of the function ψ is not equal to zero.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-012-0654-9