Title

The S-Elementary Frame Wavelets Are Path Connected

Keywords

Fourier transform; Frame wavelet sets; Frame wavelets; Frames; Wavelets

Abstract

An s-elementary frame wavelet is a function ψ ∈ L 2(ℝ) which is a frame wavelet and is defined by a Lebesgue measurable set E ⊂ ℝ such that ψ = 1/√ΧE. In this paper we prove that the family of s-elementary frame wavelets is a path-connected set in the L 2(ℝ)-norm. This result also holds for s-elementary A-dilation frame wavelets in L 2(ℝ d) in general. On the other hand, we prove that the path-connectedness of s-elementary frame wavelets cannot be strengthened to uniform path-connectedness. In fact, the sets of normalized tight frame wavelets and frame wavelets are not uniformly path-connected either.

Publication Date

9-1-2004

Publication Title

Proceedings of the American Mathematical Society

Volume

132

Issue

9

Number of Pages

2567-2575

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-04-07271-5

Socpus ID

4344611753 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/4344611753

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