Localization of Frames

Abstract

Motivated by Balan, Casazza, Heil, and Landau's results on localization of frames in a separable Hilbert space ℋ, we investigate the transitivity of localization relation of the frame ℱ = {f i } i∈I and sequence ℰ = {e j } j∈G in ℋ with respect to the associated map a: I → G, where G is a discrete abelian group and I is a index set. We also study some properties of ℓ p -column decay, ℓ p -row decay, weak homogeneous approximation property, and strong homogeneous approximation property of frame ℱ = {f i } i∈I , and sequence ℰ = {e j } j∈G , with respect to the associated map a.