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, M., & Triolo, S. (2007). An invariant analytic orthonormalization procedure with applications. JOURNAL OF MATHEMATICAL PHYSICS, 48, 103513_1-103513_15.
Data di pubblicazione: | 2007 |
Titolo: | An invariant analytic orthonormalization procedure with applications |
Autori: | |
Citazione: | Bagarello, F., Abdollahpour, M., & Triolo, S. (2007). An invariant analytic orthonormalization procedure with applications. JOURNAL OF MATHEMATICAL PHYSICS, 48, 103513_1-103513_15. |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1063/1.2800286 |
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. |
URL: | http://scitation.aip.org/content/aip/journal/jmp/48/10/10.1063/1.2800286 |
Settore Scientifico Disciplinare: | Settore MAT/07 - Fisica Matematica Settore MAT/05 - Analisi Matematica |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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