Gabor systems and almost periodic functions

Original · EN

We give a construction of Gabor type frames for suitable separable subspaces of the non-separable Hilbert spaces AP₂(R) of almost periodic functions of one variable. Furthermore we determine a non-countable generalized frame for the whole space AP₂(R). We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequencies.