43 citations · 53 across the 8 of their papers we have counts for
9 papers
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.…
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…
Direct limits, multiresolution analyses, and wavelets
Lawrence W. Baggett, Nadia S. Larsen, Judith A. Packer +2
A multiresolution analysis for a Hilbert space realizes the Hilbert space as the direct limit of an increasing sequence of closed subspaces. In a previous paper, we showed how, con…
Generalized multiresolution analyses with given multiplicity functions
Lawrence W. Baggett, Nadia S. Larsen, Kathy D. Merrill +2
Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space $\H$ that fail to be multiresolution analyses in the sense of wavelet theory because t…