A Littlewood-Paley type theorem on orthoprojectors onto wavelet subspaces
S. N. Kudryavtsev
TL;DR
This paper establishes a Littlewood-Paley type theorem for orthoprojectors onto wavelet subspaces derived from tensor product multiresolution analysis, extending classical harmonic analysis results to wavelet frameworks.
Contribution
It introduces a Littlewood-Paley type theorem for wavelet subspaces generated by tensor product multiresolution analysis, a novel extension in harmonic analysis.
Findings
Proves a Littlewood-Paley type inequality for wavelet subspaces.
Extends classical harmonic analysis results to multidimensional wavelet settings.
Provides theoretical foundation for wavelet-based analysis in multiple dimensions.
Abstract
The article proves an assertion analogous to the Littlewood-Paley theorem for the orthoprojectors onto wavelet subspaces corresponding to the multidimensional multiresolution analysis generated as tensor product of smooth finite scaling functions of one variable.
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Taxonomy
TopicsImage and Signal Denoising Methods · Mathematical Analysis and Transform Methods · Advanced Mathematical Modeling in Engineering