Explicit construction of pairs of dual multiple Fourier-like frames with compactly supported generators in L2(ℝd)

In this paper, we explicitly construct pairs of dual multiple Fourier-like frames for [Formula: see text] with compactly supported generators. We show that, under some conditions, the multiple Fourier-like system is a frame for [Formula: see text], with a dual multiple Fourier-like frame generated by explicitly given finite linear combinations of the generators. Thus, the assumption that the generators are compactly supported implies that also the dual generators are compactly supported, and the decay of the dual generators in frequency is controlled by the decay of the generators in frequency. We also relate the result to the construction of dual multi-window Gabor frames for [Formula: see text]. Finally, we provide a class of examples concerning box splines to illustrate the general theory.