# Maximal discrepancy for multiply generated shift-invariant spaces

Research paper by Hartmut Führ, Jun Xian

Indexed on: 16 Dec '15Published on: 16 Dec '15Published in: Archiv der Mathematik

#### Abstract

In this paper, we study multiply generated shift-invariant spaces V(Φ) and their invariance properties under arbitrary translations. We obtain a sufficient condition for a sharp estimate of shift-variance measure in multiply generated shift-invariant spaces, generalizing previous results from the singly generated orthonormal case to multiply generated Riesz systems. The sufficient condition is fulfilled under mild integrability and smoothness assumptions on the generators.