This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel 1/(1 − θx) in place of the celebrated exponential kernel exp(θx) of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic pseudo-variance functions correspond to free-i...

We show that the classical Hamburger moment problem can be included in the spectral theory of generalized indefinite strings. Namely, we introduce the class of Krein–Langer strings and show that there is a bijective correspondence between moment sequences and this class of generalized indefinite strings. This result can be viewed as a complement to the classical results of M. G. Krein on the co...

Our research project is in the area of noncommutative probability. Noncommutative probability emerged in the early ’80s as a very powerful tool for the study of finite operator algebras. The fundamental idea is to view a pair (A, τ), where A is a unital algebra over the complex numbers (usually endowed with a suitable norm topology), and τ is a linear, unit preserving, functional on A, as a non...

0. Introduction. In this paper two commutative, semisimple Banach algebras with involution, viz., A(G) and B(G), (called the Fourier algebra of G and the Fourier-Stieltjes algebra of G, respectively) are defined (as in [5]) for an arbitrary locally compact topological group G. [Note. As algebras A(G) and B(G) are subalgebras of the algebra of bounded continuous functions on G.] The main purpose...

A generalized Itô formula for time dependent functions of two-dimensional continuous semi-martingales is proved. The formula uses the local time of each coordinate process of the semi-martingale, left space and time first derivatives and second derivative ∇1 ∇ − 2 f only which are assumed to be of locally bounded variation in certain variables, and stochastic Lebesgue-Stieltjes integrals of two...

The Fourier and Fourier-Stieltjes algebras A(G) and B(G) of a locally compact group G are introduced and studied in 60’s by Piere Eymard in his PhD thesis. If G is a locally compact abelian group, then A(G) ≃ L(Ĝ), and B(G) ≃ M(Ĝ), via the Fourier and Fourier-Stieltjes transforms, where Ĝ is the Pontryagin dual of G. Recently these algebras are defined on a (topological or measured) groupoid an...