An invariant analytic orthonormalization procedure with applications

Details An invariant analytic orthonormalization procedure with applications An invariant analytic orthonormalization procedure with applications

2009-04-21

arxiv.org/abs/0904.3211v1

J. Math. Phys., 48 (2007)

Physics

Mathematical Physics

Scientific paper

10.1063/1.2800286

We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct $g(x)\in L^2(\Bbb{R})$ in such a way the functions $g_{\underline n}(x)=e^{ian_1x}g(x+an_2)$, $\underline n\in\Bbb{Z}^2$ and $a$ some positive real number, are mutually orthogonal. We discuss in some details the role of the lattice naturally associated to the procedure in this analysis.

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