The S-elementary frame wavelets are path connected
Abbreviated Journal Title
Proc. Amer. Math. Soc.
frames; wavelets; frame wavelets; frame wavelet sets; Fourier transform; SETS; Mathematics, Applied; Mathematics
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.
Proceedings of the American Mathematical Society
"The S-elementary frame wavelets are path connected" (2004). Faculty Bibliography 2000s. 4289.