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Gabor-like systems in L2(Rd) and extensions to wavelets

In this paper we show how to construct a certain class of orthonormal bases in L 2 (R d ) starting from one or more Gabor orthonormal bases in L 2 (R). Each such basis can be obtained acting on a single function Ψ(x) ∈ L 2 (R d ) with a set of unitary operators which operate as translation and modulation operators in suitable variables. The same procedure is also extended to frames and wavelets. Many examples are discussed.