Title

The S-elementary frame wavelets are path connected

Authors

Authors

X. Dai; Y. Diao; Q. Gu;D. Han

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Proc. Amer. Math. Soc.

Keywords

frames; wavelets; frame wavelets; frame wavelet sets; Fourier transform; SETS; Mathematics, Applied; Mathematics

Abstract

An s-elementary frame wavelet is a function psi is an element of L-2(R) which is a frame wavelet and is defined by a Lebesgue measurable set E subset of R such that (ψ) over cap = 1/root2pichiE. 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.

Journal Title

Proceedings of the American Mathematical Society

Volume

132

Issue/Number

9

Publication Date

1-1-2004

Document Type

Article

Language

English

First Page

2567

Last Page

2575

WOS Identifier

WOS:000222122200011

ISSN

0002-9939

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