Wavelet series expansion in Hardy spaces with approximate duals

In this paper, we provide sufficient conditions for the functions ψ and ϕ to be the approximate duals in the Hardy space H p ( R ) for all 0 < p ≤ 1 . Based on these conditions, we obtain the wavelet series expansion in the Hardy space H p ( R ) with the approximate duals. The important propertie...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2024, Vol.50 (2), p.563-595
Main Authors: Hur, Y., Lim, H.
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Series expansion
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Summary:In this paper, we provide sufficient conditions for the functions ψ and ϕ to be the approximate duals in the Hardy space H p ( R ) for all 0 < p ≤ 1 . Based on these conditions, we obtain the wavelet series expansion in the Hardy space H p ( R ) with the approximate duals. The important properties of our approach include the following: (i) our results work for any 0 < p ≤ 1 ; (ii) we do not assume that the functions ψ and ϕ are exact duals; (iii) we provide a tractable bound for the operator norm of the associated wavelet frame operator so that it is possible to check the suitability of the functions ψ and ϕ .
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-024-00022-z