Ap-frames and stationary random processes

Abstract

Abstract. It is known that, in general, an AP-frame is an L 2 (R)-frame and conversely. Here, in part as a consequence of the Ergodic Theorem, we prove a necessary and su cient condition for a Gabor system {g(t − k)e il(t−k) , l ∈ L = ω0Z, k ∈ K = t0Z} to be an L 2 (R)- Frame in terms of Gaussian stationary random processes. In addition, if X = (X(t))t∈R is a wide sense stationary random process, we study density conditions for the associated stationary sequences {hX, gk,li, l ∈ L, k ∈ K}.