On the construction of the orthonormal wavelet in the Hardy space H2(ℝ)

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

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