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.
Settore MAT/07 - Fisica Matematica
Settore MAT/05 - Analisi Matematica
http://scitation.aip.org/content/aip/journal/jmp/48/10/10.1063/1.2800286
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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