PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 51(65), pp. 4854 (1992) 

Coherent states and frames in the Bargman space of entire functionsM. Dostani\'c and D. Milinkovi\'cMatematicki fakultet, Beograd, YugoslaviaAbstract: 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 $$ \f_{mn}(x) =\pi^{1/4} \exp\{(1/2)\,imnab+imxa(1/2)\,(xnb)^2\}, \qquad a,b>0;\ \ ab<2\pi. $$ We prove this conjecture for $ab<2\pi$ and $b$ sufficiently large. Also, we give some applications for the Bargman space of entire functions. Classification (MSC2000): 30B50, 47A30 Full text of the article:
Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
