A finitely generated shift invariant space V is a closed subspace of L2(Rd) that can be generated by the integer translates of a finite number of functions. A set of frame generators for V is a set of functions whose integer ...

Given an arbitrary finite set of data F = {f1, ..., fm} ⊂ L2(Rd) we prove the existence and show how to construct a “small shift invariant space” that is “closest” to the data F over certain class of closed subspaces of ...

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper ...

Given a set of functions F = {f1, ..., fm} ⊂ L2 (Rd), we study the problem of finding the shift-invariant space V with n generators {φ1, ..., φn} that is "closest" to the functions of F in the sense thatV = under(arg min, ...

In this note, we solve the dynamical sampling problem for a class of shift-preserving operators L:V→V acting on a finitely generated shift-invariant space V. We find conditions on L and a finite set of functions of V so ...

In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We ...

We introduce extensions of the convex potentials for finite frames (e.g. the frame potential defined by Benedetto and Fickus) in the framework of Bessel sequences of integer translates of finite sequences in L2(Rk). We ...

For a given finitely generated shift invariant (FSI) subspace W⊂L2(Rk) we obtain a simple criterion for the existence of shift generated (SG) Bessel sequences E(F) induced by finite sequences of vectors F∈Wn that have a ...