Bargmann representation of $q$-commutation relations for $q>1$ and associated measures
Tom 78 / 2007
Banach Center Publications 78 (2007), 171-183
MSC: Primary 81S05; Secondary 30E05.
DOI: 10.4064/bc78-0-13
Streszczenie
The classical Bargmann representation is given by operators acting on the space of holomorphic functions with the scalar product $\langle z^n|z^k\rangle _q=\delta_{n,k}[n]_q!=F(z^n\overline{z}^k)$. We consider the problem of representing the functional $F$ as a measure for $q>1$. We prove the existence of such a measure and investigate some of its properties like uniqueness and radiality. The above problem is closely related to the indeterminate Stieltjes moment problem.
