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Judith A. Packer

  1. Probability measures on solenoids corresponding to fractal wavelets.

    Чт, 11/04/2010 - 16:01 — SomNambul
    Authors: Lawrence W. Baggett, Kathy D. Merrill, Judith A. Packer, Arlan B. Ramsay
    Subjects: Classical Analysis and ODEs
    Abstract

    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 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.

  2. Classification of Generalized Multiresolution Analyses.

    Чт, 10/29/2009 - 16:01 — SomNambul
    Authors: Lawrence W. Baggett, Veronika Furst, Kathy D. Merrill, Judith A. Packer
    Subjects: Classical Analysis and ODEs
    Abstract

    We 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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