In this paper, we shall discuss Bargmann type measures on C for several
classes of probability measures on R. The unified interpolation expressions include not
only the classical Bargmann measure and its q-deformation, but also their t-deformations
and dilations. As a special case, we get conditions on existence and an explicit form of the
Bargmann representation for the free Meixner family of probability measures.
Demonstratio Mathematica, founded in 1969, is a fully peer-reviewed, open access journal that publishes original and significant research works and review articles devoted to functional analysis, approximation theory, and related topics. The journal provides the readers with free, instant, and permanent access to all content worldwide (all 53 volumes are available online!)