A family of heat functions as solutions of indeterminate moment problems.
A general bounded continuous moment problem and its sets of uniqueness
A limit theorem for the q-convolution
The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
A moment sequence in the q-world
The aim of the paper is to present some initial results about a possible generalization of moment sequences to a so-called q-calculus. A characterization of such a q-analogue in terms of appropriate positivity conditions is also investigated. Using the result due to Maserick and Szafraniec, we adapt a classical description of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity to the q-situation. This makes a link between q-positive definiteness and q-complete...
A multi-dimensional Hausdorff moment problems regularization by finite moments.
A note on a problem arising from risk theory
In this note we give an answer to a problem of Gheorghiță Zbăganu that arose from the study of the properties of the moments of the iterates of the integrated tail operator.
A Pick function related to an inequality for the entropy function.
A q-analogue of complete monotonicity
The aim of this paper is to give a q-analogue for complete monotonicity. We apply a classical characterization of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity, adapted to the q-situation. The method due to Maserick and Szafraniec that does not need moments turns out to be useful. A definition of a q-moment sequence appears as a by-product.
An Algorithm for the Hausdorff Moment Problem.
An example of a positive semidefinite double sequence which is not a moment sequence
The first explicit example of a positive semidefinite double sequence which is not a moment sequence was given by Friedrich. We present an example with a simpler definition and more moderate growth as .
An extension of a Meyer's theorem
An operator-theoretic approach to truncated moment problems
We survey recent developments in operator theory and moment problems, beginning with the study of quadratic hyponormality for unilateral weighted shifts, its connections with truncated Hamburger, Stieltjes, Hausdorff and Toeplitz moment problems, and the subsequent proof that polynomially hyponormal operators need not be subnormal. We present a general elementary approach to truncated moment problems in one or several real or complex variables, based on matrix positivity and extension. Together...
Asymptotic behavior of moment sequences.
Backward extensions of hyperexpansive operators
The concept of k-step full backward extension for subnormal operators is adapted to the context of completely hyperexpansive operators. The question of existence of k-step full backward extension is solved within this class of operators with the help of an operator version of the Levy-Khinchin formula. Some new phenomena in comparison with subnormal operators are found and related classes of operators are discussed as well.
Concerning local flatness in the moment problem
Corrigendum to "The Moment Problem in the Space C...(S)''.
Ein Pólyasches Momentenproblem und umhüllende asymptotische Potenzreihen.
Erratum: On the positive definiteness of n (a sequence of exponentials).
Extreme positive definite double sequences which are not moment sequences.
From the fact that the two-dimensional moment problem is not always solvable, we can deduce that there must be extreme ray generators of the cone of positive definite double sequences which are nor moment sequences. Such an argument does not lead to specific examples. In this paper it is shown how specific examples can be constructed if one is given an example of an N-extremal indeterminate measure in the one-dimensional moment problem (such examples exist in the literature). Konrad Schmüdgen had...
Fuss-Catalan numbers in noncommutative probability.