The S-elementary frame wavelets are path connected

    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

    Share

    COinS