Generalized Multiresolution Analyses with Given Multiplicity Functions |
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Authors: | Lawrence W Baggett Nadia S Larsen Kathy D Merrill Judith A Packer Iain Raeburn |
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Institution: | 1. Department of Mathematics, University of Colorado, Boulder, CO, 80309, USA 2. Department of Mathematics, University of Oslo, Blindern, 0316, Oslo, Norway 3. Department of Mathematics, Colorado College, Colorado Springs, CO, 80903, USA 4. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia
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Abstract: | 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 the core subspace does not have an orthonormal basis generated by a fixed
scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space ℋ is L
2(ℝ
n
), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition, which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity
function m. |
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Keywords: | |
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