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 psi((x) under bar) is an element of 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.