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arXiv · 0904.0898

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

F. Bagarello
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Abstract

In this paper we show how to construct a certain class of orthonormal bases in $L^2({\bf R}^d)$ starting from one or more Gabor orthonormal bases in $L^2({\bf R})$. Each such basis can be obtained acting on a single function $Ψ(\underline x)\in L^2({\bf R}^d)$ 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.

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F. Bagarello. 2009-04-06. Gabor-like systems in $L^2({\bf R}^d)$ and extensions to wavelets. https://doi.org/10.1088/1751-8113/41/33/335208

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