Frames of translates with prescribed fine structure in shift invariant spaces

2015/12/22 by Benac, Maria Jose, Massey, Pedro, Stojanoff, Demetrio
#42C15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1512.07122

Abstract

For a given finitely generated shift invariant (FSI) subspace \cW⊂ L²(\R^k) we obtain a simple criterion for the existence of shift generated (SG) Bessel sequences E(\cF) induced by finite sequences of vectors \cF∈ \cWⁿ that have a prescribed fine structure i.e., such that the norms of the vectors in \cF and the spectra of S_E(\cF) is prescribed in each fiber of Spec(\cW)⊂ \T^k. We complement this result by developing an analogue of the so-called sequences of eigensteps from finite frame theory in the context of SG Bessel sequences, that allows for a detailed description of all sequences with prescribed fine structure. Then, given 0

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• Construction of frames for shift-invariant spaces
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• Shift-invariant subspaces of Sobolev type