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Interpolations of Bargmann type measures

Asai N., Krystek A. D., Wojakowski Ł. J.

Demonstratio Mathematica

2016

Vol. 49, nr 3

293--301

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.

Bargmann measures for t-deformed probability

Krystek A. D., Wojakowski Ł. J.

Probability and Mathematical Statistics

2014

Vol. 34, Fasc. 2

279--291

It is shown that the Bargmann representation of a t-deformed probability measure can be obtained by taking away some t-dependent amount of mass at zero of the Bargmann representation of the original measure and scaling of the remaining part. This allows us to formulate conditions on existence of the Bargmann representation of a t-deformed probability measure and to study some prominent examples.