We present a general approach to a module frame theory in Câˆ—algebras and Hilbert Câˆ—-modules. The investigations rely on the ideas of geometric dilation to standard Hilbert Câˆ—-modules over unitalâ€¦ (More)

A congruency theorem is proven for an ordered pair of groups of homeomorphisms of a metric space satisfying an abstract dilation-translation relationship. A corollary is the existence of waveletâ€¦ (More)

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*modules. The reported investigations rely on the idea of geometric dilation toâ€¦ (More)

Abstract. The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides aâ€¦ (More)

We use several fundamental results which characterize frames for a Hilbert space to give natural generalizations of Hilbert space frames to general Banach spaces. However, we will see that all ofâ€¦ (More)

We present a new approach to characterizing (multi)wavelets by means of basic equations in the Fourier domain. Our method yields an uncomplicated proof of the two basic equations and a newâ€¦ (More)

We discuss three applications of operator algebra techniques in Gabor analysis: the parametrizations of Gabor frames, the incompleteness property, and the unique Gabor dual problem for subspace Gaborâ€¦ (More)

Let Î¨ = {Ïˆ1, . . . , ÏˆL} âŠ‚ L2 := L2(âˆ’âˆž,âˆž) generate a tight affine frame with dilation factor M , where 2 â‰¤M âˆˆ Z, and sampling constant b = 1 (for the zeroth scale level). Then for 1 â‰¤ N âˆˆ Z,â€¦ (More)

We prove that, as in the case of global actions, any partial action gives rise to a groupoid provided with a Haar system, whose Câˆ—-algebra agrees with the crossed product by the partial action.

Multiresolution structures are important in applications, but they are also useful for analyzing properties of associated wavelets. Given a nonorthogonal (multi-) wavelet in a Hilbert space, weâ€¦ (More)