Biorthogonal wavelets, MRA's and shift-invariant spaces
Volume 160 / 2004
Studia Mathematica 160 (2004), 231-248 MSC: Primary 42C40. DOI: 10.4064/sm160-3-3
We give a characterization of biorthogonal wavelets arising from MRA's of multiplicity $D$ entirely in terms of the dimension function. This improves the previous characterization in  removing an unnecessary angle condition. Besides we characterize Riesz wavelets arising from MRA's, and present new proofs based on shift-invariant space theory, generalizing the 1-dimensional results appearing in .