Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ

Abstract

We consider the multigenerator system {EmblTnalφl,m,n∈ℤ, l=0,…,r-1} for φ0,…,φr-1∈L2(𝕊) and a0,b0,…,ar-1, br-1>0, where the parameters b0,…,br-1>0 are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame for L2(𝕊). Moreover, we present some characterizations for this system to be a Parseval frame.