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In this paper, we devote our interest to solving the real cubic truncated moment problem. We provide some results that allow to get a complete solution via a minimal representing measure. Some numerical examples are also presented to…
We study the truncated multidimensional moment problem with a general type of truncations. The operator approach to the moment problem is presented. A way to construct atomic solutions of the moment problem is indicated.
We consider the explicit relation between two resolvent matrices related to the truncated Hausdorff matrix moment problem (THMM) in the case of an even and odd number of moments. This relation is described with the help of four families of…
Truncated moment problems in the class of generalized Nevanlinna functions are investigated. General solvability criteria will be established, covering both the even and odd problems, including complete parametrizations of solutions. The…
A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing…
These notes contain a presentation of the noncommutative generalization of the classical moment problem introduced in [10] and [12]. They also contain a short summary of the classical moment problem in infinite dimension.
For the truncated multidimensional moment problem we introduce a notion of a canonical solution. Namely, canonical solutions are those solutions which are generated by commuting self-adjoint extensions inside the associated Hilbert space.…
This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix…
When the algebraic variety associated with a truncated moment sequence is finite, solving the moment problem follows a well-defined procedure. However, moment problems involving infinite algebraic varieties are more complex and less…
In this paper we study the truncated power moment problem with an odd number of prescribed moments. A Nevanlinna-type formula is derived for this moment problem in the case when the moment problem has more than one solution (the…
In recent years, the so-called polynomial moment problem, motivated by the classical Poincare center-focus problem, was thoroughly studied, and the answers to the main questions have been found. The study of a similar problem for rational…
The main goal of this paper is to reconsider a phenomenon which was treated in earlier work of the authors' on several truncated matricial moment problems. Using a special kind of Schur complement we obtain a more transparent insight into…
We introduce a new strategy in solving the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed \emph{moment}…
In this paper we obtain a description of all solutions of truncated matricial moment problems on a finite interval in a general case (no conditions besides solvability are assumed). We use the basic results of M.G. Krein and I.E. Ovcharenko…
We present an alternative solution to nonsingular cubic moment problems, using techniques that are expected to be useful for higher-degree truncated moment problems. In particular, we apply the theory of recursively determinate moment…
A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…
This paper is a continuation of our previous investigation on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no.6, 786-797. In the present paper we obtain a Nevanlinna-type formula for this moment problem…
Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…
The truncated moment problem asks to characterize finite sequences of real numbers that are the moments of a positive Borel measure on Rn. Its tracial analog is obtained by integrating traces of symmetric matrices and is the main topic of…
In this paper we study the truncated matrix trigonometric moment problem. We obtained a bijective parameterization of all solutions of this moment problem (both in nondegenerate and degenerate cases) via an operator approach. We use…