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.
2007
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/8847
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