43 citations · 52 across the 9 of their papers we have counts for
10 papers
Wavelet sets for crystallographic groups
Kathy D. Merrill
Single wavelet sets, and thus single wavelets, are shown to exist for the actions of all crystallographic groups on under all integer dilations. Examples of such sets…
Decomposing the wavelet representation for shifts by wallpaper groups
Lawrence W. Baggett, Kathy D. Merrill, Judith A. Packer +1
The wavelet group and wavelet representation associated with shifts coming from a two dimensional crystal symmetry group and dilations by powers of 3, are defined and studied.…
Simple wavelet sets in R^n
Kathy D. Merrill
Wavelet sets that are finite unions of convex sets are constructed in , , for dilation by any expansive matrix that has a power equal to a scalar times the id…
Probability measures on solenoids corresponding to fractal wavelets
Lawrence W. Baggett, Kathy D. Merrill, Judith A. Packer +1
The measure on generalized solenoids constructed using filters by Dutkay and Jorgensen is analyzed further by writing the solenoid as the product of a torus and a Cantor set. Using…
Classification of Generalized Multiresolution Analyses
Lawrence W. Baggett, Veronika Furst, Kathy D. Merrill +1
We discuss how generalized multiresolution analyses (GMRAs), both classical and those defined on abstract Hilbert spaces, can be classified by their multiplicity functions and…
Generalized low-pass filters and multiresolution analyses
Lawrence W. Baggett, Veronika Furst, Kathy D. Merrill +1
We study generalized filters that are associated to multiplicity functions and homomorphisms of the dual of an abelian group. These notions are based on the structure of generalize…