Frame wavelets with frame set support in the frequency domain

Abstract

In this paper, we study a special class of frame wavelets. The supports of the Fourier transforms of these frame wavelets are the so called frame wavelet sets. Our results provide ways to construct frame wavelets not known previously. In particular, for any given positive number $\alpha$, we show that there exist various frame wavelets whose Fourier transforms are supported by a set of measure $\alpha$.