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RESEARCH PRODUCT
An invariant analytic orthonormalization procedure with applications
Fabio BagarelloSalvatore TrioloM. R. Abdollahpoursubject
PhysicsLattice (group)FOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)CombinatoricsSettore MAT/05 - Analisi MatematicaCoherent statesInvariant (mathematics)Connection (algebraic framework)Gabor framesSettore MAT/07 - Fisica MatematicaMathematical PhysicsReal numberdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-10-01 |