Construction of frames for shift-invariant spaces

Abstract

We construct a sequence φi(·-j)j∈, i=1, r which constitutes a p-frame for the weighted shift-invariant space Vp(Φ)= i=1r jci(j)φi(·-jci(j)jp, i=1, r, p∈[1,∞], and generates a closed shift-invariant subspace of Lp(R). The first construction is obtained by choosing functions φi, i=1,r, with compactly supported Fourier transforms φi, i=1,.,r. The second construction, with compactly supported φi, i=1,r, gives the Riesz basis. © 2013 Stevan Pilipović and Suzana Simić.