Classical Bargmann’s representation is given by operators acting on the space of holomorphic functions with scalar product $〈z^n,z^k{〉}_q={\delta }_{n,k}{\left[n\right]}_q!=F\left(z^n{\overline{z}}^k\right)$. We consider the problem of representing the functional F as a measure. We prove the existence of such a measure for q > 1 and investigate some of its properties like uniqueness and radiality.

The Pompeiu and the Morera problems have been studied in many contexts and generality. For example in different spaces, with different groups, locally, without an invariant measure, etc. The variations obtained exhibit the fascination of these problems.In this paper we present a new aspect: we study the case in which the functions have values over a Clifford Algebra. We show that in this context it is completely natural to consider the Morera problem and its variations. Specifically, we show the...