2007/10/10 by Lawrence W. Baggett, Nadia S. Larsen, Baggett, Lawrence W. +7
Computer Science · Earth and Planetary Sciences · Mathematics · #42C40 #47D03 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.0710.2071
openalex publication_date 2007/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 L2(\mathbb Rn), 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.