Frames for Weighted Shift-invariant Spaces

Abstract

In this paper we prove the equivalence of the frame property and the closedness for a weighted shift-invariant space which corresponds to Φ = Φr = (Ø1, Ø2, ... Ør)T ∈ (Wω1)r. We, also, construct a sequence Φ2k+1 and the sequence of spaces VΜp(Φ2k+1),k ∈ ℕ, on ℝ with the useful properties in sampling, approximations and stability. © 2011 Springer Basel AG.