Title
The S-elementary frame wavelets are path connected
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
ISSN
0002-9939
Recommended Citation
"The S-elementary frame wavelets are path connected" (2004). Faculty Bibliography 2000s. 4289.
https://stars.library.ucf.edu/facultybib2000/4289
Comments
Authors: contact us about adding a copy of your work at STARS@ucf.edu