Orthogonal Frames of Translates

Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have the form of translates of a finite number of functions in \ltwod. The characterizations are applied to Bessel sequences which have an affine structure, and a quasi-affine structure. These also lead to characterizations of superframes. Moreover, we characterize perfect reconstruction, i.e. duality, of subspace frames for translation invariant (bandlimited) subspaces of \ltwod.Comment: 20 page

Applications of the Wavelet Multiplicity Function

This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet connectivity problem.Comment: 9 pages, AMS-Late