Geodesic
Coherent States and Frames in the Bargman Space of Entire Functions
Publications de l'Institut Mathématique, _N_S_51 (1992) no. 65, p. 48 .

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A conjecture was given in [3] about the possibility of decomposition of an arbitrary $f$ in $L^2(R)$ in terms of the family of functions $ \f_{mn}(x) =\pi^{-1/4} \exp\{-(1/2) imnab+imxa-(1/2) (x-nb)^2\}, \qquad a,b>0; ab2\pi. $ We prove this conjecture for $ab2\pi$ and $b$ sufficiently large. Also, we give some applications for the Bargman space of entire functions.
Classification : 30B50 47A30 
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     author = {Milutin Dostani\'c and Darko Milinkovi\'c},
     title = {Coherent {States} and {Frames} in the {Bargman} {Space} of {Entire} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
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     year = {1992},
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Milutin Dostanić; Darko Milinković. Coherent States and Frames in the Bargman Space of Entire Functions. Publications de l'Institut Mathématique, _N_S_51 (1992) no. 65, p. 48 . http://geodesic.mathdoc.fr/item/PIM_1992_N_S_51_65_a4/