Related papers: On the truncated multidimensional moment problems …
We characterize the existence of the Lebesgue integrable solutions of the truncated problem of moments in several variables on unbounded supports by the existence of some maximum entropy -- type representing densities and discuss a few…
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…
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…
This paper is about the moment problem on a finite-dimensional vector space of continuous functions. We investigate the structure of the convex cone of moment functionals (supporting hyperplanes, exposed faces, inner points) and treat…
In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we…
This paper deals with the moment problem on a (not necessarily finitely generated) commutative unital real algebra $A$. We define moment functionals on $A$ as linear functionals which can be written as integrals over characters of $A$ with…
The truncated multidimensional moment problem is studied in terms of the Stieltjes transform as the interpolation problem. A step-by-step algorithm is constructed for the multidimensional moment problem and the set of solutions is found in…
We propose convex optimization algorithms to recover a good approximation of a point measure $\mu$ on the unit sphere $S\subseteq \mathbb{R}^n$ from its moments with respect to a set of real-valued functions $f_1,\dots, f_m$. Given a finite…
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…
Let $\tau$ be a locally convex topology on the countable dimensional polynomial $\reals$-algebra $\rx:=\reals[X_1,...,X_n]$. Let $K$ be a closed subset of $\reals^n$, and let $M:=M_{\{g_1, ... g_s\}}$ be a finitely generated quadratic…
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}…
The multidimensional moment problem is studied in terms of the Steiltjes transform. The diagonal step-by-step algorithm is constructed for the multidimensional moment problem. The set of solutions of the full multidimensional moment problem…
The strong truncated Hamburger moment problem (STHMP) of degree $(-2k_1,2k_2)$ asks to find necessary and sufficient conditions for the existence of a positive Borel measure, supported on $\mathbb{R}\setminus \{0\}$, such that $\beta_i=\int…
A long series of previous papers have been devoted to the (one-dimensional) moment problem with nonnegative rational measure. The rationality assumption is a complexity constraint motivated by applications where a parameterization of the…
The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher…
The generalized moment problem (GMP) is an infinite dimensional linear problem over the cone of finite nonnegative Borel measures. When a GMP instance involves finitely many polynomial moment constraints, moment/sum-of-squares hierarchies…
In this paper we introduce the theory of derivatives of moments and (moment) functionals to represent moment functionals by Gaussian mixtures, characteristic functions of polytopes, and simple functions of polytopes. We study, among other…
This note aims to show a uniqueness property for the solution (whenever exists) to the moment problem for the symmetric algebra $S(V)$ of a locally convex space $(V, \tau)$. Let $\mu$ be a measure representing a linear functional $L:…
The multivariate moment problem is investigated in the general context of the polynomial algebra $\mathbb{R}[x_i \mid i \in \Omega]$ in an arbitrary number of variables $x_i$, $i\in \Omega$. The results obtained are sharpest when the index…