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Beurling’s and Wiener’s theory of spectral synthesis of Banach algebras can be formulated as an approximation theory where the approximants of a function f are required to be supported within the support of f. This is not the case for $$L^2$$ wavelet theory. On the other hand, there are applications in which wavelets can play a role where such support constraints are necessary. For Haar wavelets, it is proved in a constructive, computable way that such approximation can be effected for $$L^p$$ , $$0

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An Applicable Variant of Spectral Synthesis for Wavelets

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  • 发表日期：

    2025年

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  • John J. Benedetto

摘要

Beurling’s and Wiener’s theory of spectral synthesis of Banach algebras can be formulated as an approximation theory where the approximants of a function f are required to be supported within the support of f. This is not the case for $$L^2$$ wavelet theory. On the other hand, there are applications in which wavelets can play a role where such support constraints are necessary. For Haar wavelets, it is proved in a constructive, computable way that such approximation can be effected for $$L^p$$ , $$0