On wavelet induced isomorphisms for reducing subspaces

摘要

In this paper, we adapt the notion of a wavelet induced isomorphism of [0, 1) associated with a wavelet set, introduced in [E. J. Ionascu, A new construction of wavelet sets, Real Anal. Exchange 28(2) (2002/03) 593-610], to the case of an H-wavelet set, where H is a reducing subspace [X. Dai and S. Lu, Wavelets in subspaces, Michigan Math. J. 43 (1996) 81-98]. We characterize all these wavelet induced isomorphisms similar to those given in Ionascu paper and provide specific examples of this theory in the case of symmetric H-wavelet sets. Examples when H is the classical Hardy space are also considered.