Linear combinations of generators in multiplicatively invariant spaces

Bounded generators of linear spaces

Multi-Channel Sampling on Shift-Invariant Spaces with Frame Generators

Let φ be a continuous function in L(R) such that the sequence {φ(t− n)}n∈Z is a frame sequence in L(R) and assume that the shift-invariant space V (φ) generated by φ has a multi-banded spectrum σ(V ). The main aim in this paper is to derive a multi-channel sampling theory for the shift-invariant space V (φ). By using a type of Fourier duality between the spaces V (φ) and L[0, 2π] we find necess...

Optimal Shift Invariant Spaces and Their Parseval Frame Generators

Given a set of functions F = {f1, . . . , fm} ⊂ L2(R), 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 that V = argminV ′∈Vn m X i=1 wi‖fi − PV ′fi‖, where wis are positive weights, and Vn is the set of all shift-invariant spaces that can be generated by n or less generators. The Eckart-Young The...

Duality in spaces of finite linear combinations of atoms

In this note we describe the dual and the completion of the space of finite linear combinations of (p,∞)-atoms, 0 < p ≤ 1. As an application, we show an extension result for operators uniformly bounded on (p,∞)-atoms, 0 < p < 1, whose analogue for p = 1 is known to be false. Let 0 < p < 1 and let T be a linear operator defined on the space of finite linear combinations of (p,∞)-atoms, 0 < p < 1...

Nillsen Difference Spaces and Invariant Linear Forms