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(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.
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