Related papers: The Nevanlinna-type formula for the truncated matr…
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…
This paper deals with (1) the truncated matrix Hamburger moment problem from the point of view of reproducing kernel Hilbert spaces of vector valued entire functions of the kind introduced and extensively studied by Louis de Branges and (2)…
In this article we study the bivariate truncated moment problem (TMP) of degree $2k$ on reducible cubic curves. First we show that every such TMP is equivalent after applying an affine linear transformation to one of 8 canonical forms of…
The main goal of this paper is to achieve a simultaneous treatment of the even and odd truncated matricial Hamburger moment problems in the most general case. In the odd case, these results are completely new for the matrix case, whereas…
In this article we study the bivariate truncated moment problem (TMP) of degree $2k$ on the union of parallel lines. First we present an alternative proof of Fialkow's solution \cite{Fia15} to the TMP on the union of two parallel lines…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
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.…
In this paper we consider two related objects: singular positive semidefinite Hankel block--matrices and associated degenerate truncated matrix Hamburger moment problems. The description of all solutions of a degenerate matrix Hamburger…
The main goal of the paper is to parametrize the Weyl matrix balls associated with an arbitrary matricial truncated Hamburger moment problem. For the special case of a non-degenerate matricial truncated Hamburger moment problem the…
Nevanlinna-Pick interpolation and moment problems use the analytic structures provided by causality in order to provide rigorous bounds on smeared spectral functions. This proceedings discusses Nevanlinna-Pick interpolation and moment…
In this article we solve four special cases of the truncated Hamburger moment problem (THMP) of degree $2k$ with one or two missing moments in the sequence. As corollaries we obtain, by using appropriate substitutions, the solutions to…
This paper is about the general truncated matrix-valued moment problem. Let $\mathcal{H}_q$ denote the complex Hermitian $q\times q$-matrices, $q\in \mathbb{N}$. Suppose that $(\mathcal{X},\mathfrak{X})$ is a measurable space and…
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}…
A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form $\dot x_1=u$, $\dot x_j=x_1^{j-1}$, $j=2,\ldots,n$, is obtained for arbitrary $n$. The main goal of the paper is to present the…
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…
The technique of truncated moments of parton distributions allows us to study scaling violations without making any assumption on the shape of parton distributions. The numerical implementation of the method is however difficult, since the…
This German paper discusses certain aspects of the non-degenerate case of truncated matricial moment problems on the intervals [$\alpha$,$\infty$) and (-$\infty$,\alpha] for any real number $\alpha$.
We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a…
We characterize the existence of the $L^1$ solutions of the truncated moments problem in several real variables on unbounded supports by the existence of the maximum of certain concave Lagrangian functions. A natural regularity assumption…
In this paper we study truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint and $J$-unitary operators. Conditions of the solvability are given. Some canonical solutions of the moment problems are constructed. As a…