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An interplay between Gabor and Wilson frames. (English) Zbl 1286.42046

Summary: Wilson frames \(\{\psi_j^k : w_0, w_{-1} \in L^2(\mathbb R)\}_{j\in \mathbb Z, k \in \mathbb N_0}\) as a generalization of Wilson bases have been defined and studied. We give necessary condition for a Wilson system to be a Wilson frame. Also, sufficient conditions for a Wilson system to be a Wilson Bessel sequence are obtained. Under the assumption that the window functions \(w_{0}\) and \(w_{-1}\) for odd and even indices of \(j\) are the same, we obtain sufficient conditions for a Wilson system to be a Wilson frame (Wilson Bessel sequence). Finally, under the same conditions, a characterization of Wilson frame in terms of Zak transform is given.

MSC:

42C15 General harmonic expansions, frames
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