Gabor-like systems in $L^2({\mathbf{R}}^d)$ and extensions to wavelets

Abstract

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

References in corpus (3)

• An invariant analytic orthonormalization procedure with applications
• An invariant analytic orthonormalization procedure with an application to coherent states
• Relations between multi-resolution analysis and quantum mechanics