Frames of translates with prescribed fine structure in shift invariant spaces

DEMETRIO STOJANOFF; DEMETRIO STOJANOFF; MARÍA JOSÉ BENAC; MARÍA JOSÉ BENAC; PEDRO MASSEY; PEDRO MASSEY

JOURNAL OF FUNCTIONAL ANALYSIS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2016 vol. 271 p. 2631 - 2671

0022-1236

For a given finitely generated shift invariant (FSI) subspace $cWsubset L^2(R^k)$ we obtain a simple criterion for the existence of shift generated (SG) Bessel sequences $E(cF)$ induced by finite sequences of vectors $cFin cW^n$ 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 $ext{Spec}(cW)subset T^k$. 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