GENERATING NEW FRAMES IN L2(R) BY CONVOLUTIONS

Abstract

Let c = fcngn∈Z 2 ℓ1(Z) and ffngn∈Z be a frame (Riesz basis, respectively) of L2(R). We obtain necessary and sufficient conditions on c under which fc fngn∈Z becomes a frame (Riesz basis, respectively) of L2(R), where λ > 0 and (c f)(t) := Σn∈Z cnf(t􀀀 nλ). When fc fngn∈Z becomes a frame of L2(R), we present its frame operator and the canonical dual frame in a simple form. Some interesting examples are included.