The S-elementary frame wavelets are path connected

摘要

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.