An invariant analytic orthonormalization procedurewith applications

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 g n ̱ ( x ) = e i a n 1 x g ( x + a n 2 ) , n ̱ ∊ Z 2 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.