Publication Type
Journal
Journal Name
Journal of Mathematical Analysis and Applications
Publication Date
Page Numbers
1059 to 1084
Volume
478
Issue
2
Abstract
We investigate systems of the form {At g : g ∈ G, t ∈ [0, L]} where A ∈ B(H) is a normal operator in a separable Hilbert space H, G ⊂ H is a countable set, and L is a positive real number. Although the main goal of this work is to study the frame properties of {At g : g ∈ G, t ∈ [0, L]}, as intermediate steps, we explore the completeness and Bessel properties of such systems from a theoretical perspective, which are of interest by themselves. Beside the theoretical appeal of investigating such systems, their connections to dynamical and mobile sampling make them fundamental for understanding and solving several major problems in engineering and science.