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Abstract

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.