Judith A. Packer
Probability measures on solenoids corresponding to fractal wavelets.
Thu, 11/04/2010 - 16:01 — SomNambulAuthors: Lawrence W. Baggett, Kathy D. Merrill, Judith A. Packer, Arlan B. Ramsay
Subjects: Classical Analysis and ODEs
AbstractThe 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 this decomposition, key differences are revealed
between solenoid measures associated with classical filters in $\mathbb R^d$
and those associated with filters on inflated fractal sets.Classification of Generalized Multiresolution Analyses.
Thu, 10/29/2009 - 16:01 — SomNambulAuthors: Lawrence W. Baggett, Veronika Furst, Kathy D. Merrill, Judith A. Packer
Subjects: Classical Analysis and ODEs
AbstractWe discuss how generalized multiresolution analyses (GMRAs), both classical
and those defined on abstract Hilbert spaces, can be classified by their
multiplicity functions $m$ and matrix-valued filter functions $H$. Given a
natural number valued function $m$ and a system of functions encoded in a
matrix $H$ satisfying certain conditions, a construction procedure is described
that produces an abstract GMRA with multiplicity function $m $ and filter
system $H$. An equivalence relation on GMRAs is defined and described in terms
of their associated pairs $(m,H)$.
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