Frames by Iterations in Shift-invariant Spaces

AGUILERA AGUILERA, ALEJANDRA; PATERNOSTRO, VICTORIA; CARBAJAL, DIANA; CARLOS CABRELLI

Bordeaux

Congreso; 13th International conference on Sampling Theory and Applications (SampTA); 2019

Université de Bordeaux

In this note we solve the dynamical sampling problemfor a class of shift-preserving (SP) operators, acting on afinitely generated shift-invariant space (FSIS). We find conditionson the operator and on a finite set of functions in the FSIS inorder that the iterations of the operator on the functions producea frame generator set. That is, the integer translations of theframe generator set is a frame of the FSIS. In order to obtainthese results, we study the structure of SP operators and obtaina generalized finite dimensional spectral theorem.