New Approaches to Duals of Fourier-Like Systems

The sequences of the form fEmbgngm;n2Z, where Emb is the modulation operator, b > 0 and gn is the window function in L2(R), construct Fourier-like systems. We try to consider some sucient conditions on the window functions of Fourier-like systems, to make a frame and nd a dual frame with the same structure. We also extend the given two Bessel Fourier-like systems to make a pair of dual frames and prove that the window functions of Fourier-like Bessel sequences share the compactly supported property with their extensions. But for polynomials windows, a result of this type does not happen.