Frame wavelet sets in Rd

In this paper, we discuss the characterization of frame wavelet sets. We extend some results obtained earlier in the one-dimensional case. More specifically, we completely characterize tight frame wavelet sets in higher dimensions and obtain some necessary conditions and sufficient conditions for a set E to be a frame wavelet set in Rd. Several examples are presented and compared with those in the one-dimensional case. Using our results, one can easily construct various frame wavelet sets.