We apply the orthonormalization procedure previously introduced by Bagarello and Triolo [J. Math. Phys. 48, 043505 (2007)] 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) ∈ L 2(ℝ) in such a way the functions gn(x)=e ian1xg(x+an2), n ∈ ℤ2 and a some positive real number, are mutually orthogonal. We discuss in some detail the role of the lattice naturally associated with the procedure in this analysis.
BAGARELLO F, ABDOLLAHPOUR MR, TRIOLO S (2007). An invariant analytic orthonormalization procedure with applications. JOURNAL OF MATHEMATICAL PHYSICS, 48, 103513_1-103513_15 [10.1063/1.2800286].
An invariant analytic orthonormalization procedure with applications
BAGARELLO, Fabio;TRIOLO, Salvatore
2007-01-01
Abstract
We apply the orthonormalization procedure previously introduced by Bagarello and Triolo [J. Math. Phys. 48, 043505 (2007)] 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) ∈ L 2(ℝ) in such a way the functions gn(x)=e ian1xg(x+an2), n ∈ ℤ2 and a some positive real number, are mutually orthogonal. We discuss in some detail the role of the lattice naturally associated with the procedure in this analysis.
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