Weak Gabor bi-frames on periodic subsets of the real line

摘要

In this paper, we introduce the concept of weak Gabor bi-frame (WGBF) in a general closed subspace M of L-2(R). It is a generalization of Gabor bi-frame, and is new even if M = L-2(R). A WGBF for M contains all information of M to some extent. Let a, b > 0, and S be an aZ-periodic subset of R with positive measure. This paper is devoted to characterizing WGBFs for L-2(S) of the form