On the construction of the orthonormal wavelet in the Hardy space H2(ℝ)
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Published:2021-10-06
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Volume:
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ISSN:0219-6913
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Container-title:International Journal of Wavelets, Multiresolution and Information Processing
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language:en
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Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.
Author:
Hashimoto Hirofumi1ORCID,
Kinoshita Tamotu1
Affiliation:
1. Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
Abstract
We are concerned with the orthonormal wavelet [Formula: see text] in the Hardy space [Formula: see text] which is a closed subspace of [Formula: see text] without negative frequency components. It is well known that there does not exist an [Formula: see text]-wavelet such that [Formula: see text] is continuous on [Formula: see text] and satisfies [Formula: see text] for some [Formula: see text]. The aim of this paper is to find a critical decay rate in the existing [Formula: see text]-wavelet under the condition that [Formula: see text] is continuous on [Formula: see text]. Moreover, we also construct a concrete [Formula: see text]-wavelet having infinite vanishing moments.
Funder
Japan Society for the Promotion of Science
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Information Systems,Signal Processing