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In this paper we improve the bounds for the Carath\'eodory number, especially on algebraic varieties and with small gaps (not all monomials are present). We provide explicit lower and upper bounds on algebraic varieties, $\mathbb{R}^n$, and…

Functional Analysis · Mathematics 2021-07-20 Philipp J. di Dio , Mario Kummer

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…

Optimization and Control · Mathematics 2020-07-07 Grigory M. Sklyar , Svetlana Yu. Ignatovich

Given a closed subset $K$ in $\mathbb{R}$, the rational $K$-truncated moment problem ($K$-RTMP) asks to characterize the existence of a positive Borel measure $\mu$, supported on $K$, such that a linear functional $\mathcal{L}$, defined on…

Functional Analysis · Mathematics 2024-11-19 Rajkamal Nailwal , Aljaž Zalar

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…

Classical Analysis and ODEs · Mathematics 2023-02-28 Abdon E. Choque-Rivero , Monika Winklmeier

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…

Functional Analysis · Mathematics 2019-10-22 Raul E. Curto , Seonguk Yoo

This paper gives via Stieltjes transform a complete description of the solution set of a matricial truncated Stieltjes-type power moment problem in the non-degenerate and degenerate cases. The approach is based on the Schur type algorithm…

Complex Variables · Mathematics 2017-07-20 Bernd Fritzsche , Bernd Kirstein , Torsten Schröder , Conrad Mädler

The truncated moment problem consists of determining whether a given finitedimensional vector of real numbers y is obtained by integrating a basis of the vector space of polynomials of bounded degree with respect to a non-negative measure…

Algebraic Geometry · Mathematics 2023-02-15 Didier Henrion , Simone Naldi , Mohab Safey El Din

In this prelinimary version of paper, we propose to give a complete solution to the Truncated Multidimensional Trigonometric Moment Problem (TMTMP) from a system and signal processing perspective. In mathematical TMTMPs, people care about…

Optimization and Control · Mathematics 2026-01-14 Guangyu Wu , Anders Lindquist

In this paper we obtain a Nevanlinna-type formula for the matrix Hamburger moment problem in a general case. We only assume that the problem is solvable and has more that one solution. We express the matrix coefficients of the corresponding…

Functional Analysis · Mathematics 2012-01-27 Sergey M. Zagorodnyuk

Let A be a finite subset of N^n, and K be a compact semialgebraic set in R^n. An A-tms is a vector y indexed by elements in A. The A-truncated K-moment problem (A-TKMP) studies whether a given A-tms y admits a K-measure or not. This paper…

Functional Analysis · Mathematics 2014-08-29 Jiawang Nie

The main goal of this paper is to achieve a simultaneous treatment of the even and odd truncated matricial Stieltjes moment problems in the most general case. These results are generalizations of results of Chen and Hu [5,17] which…

Complex Variables · Mathematics 2016-04-27 Bernd Fritzsche , Bernd Kirstein , Conrad Mädler

The paper treats several aspects of the truncated matricial $[\alpha,\beta]$-Hausdorff type moment problems. It is shown that each $[\alpha,\beta]$-Hausdorff moment sequence has a particular intrinsic structure. More precisely, each element…

Complex Variables · Mathematics 2017-01-26 Bernd Fritzsche , Bernd Kirstein , Conrad Mädler

This paper studies generalized truncated moment problems with unbounded sets. First, we study geometric properties of the truncated moment cone and its dual cone of nonnegative polynomials. By the technique of homogenization, we give a…

Numerical Analysis · Mathematics 2022-08-02 Lei Huang , Jiawang Nie , Ya-Xiang Yuan

For the truncated moment problem associated to a complex sequence $\gamma ^{(2n)}=\{\gamma _{ij}\}_{i,j\in Z_{+},i+j \leq 2n}$ to have a representing measure $\mu $, it is necessary for the moment matrix $M(n)$ to be positive semidefinite,…

Functional Analysis · Mathematics 2014-02-04 Raul E. Curto , Seonguk Yoo

We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of…

Mathematical Physics · Physics 2021-11-16 Alexander Serebryakov , Nick Simm , Guillaume Dubach

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…

Functional Analysis · Mathematics 2023-07-25 Abdelaziz El Boukili , Amar Rhazi , Bouazza El Wahbi

The paper gives a parametrization of the solution set of a matricial Stieltjes-type truncated power moment problem in the non-degenerate and degenerate cases. The key role plays the solution of the corresponding system of Potapov's…

Classical Analysis and ODEs · Mathematics 2017-12-25 B. Fritzsche , B. Kirstein , C. Mädler , T. Makarevich

We study a truncated two-dimensional moment problem in terms of the Stieltjes transform. The set of the solutions is described by the Schur step-by-step algorithm, which is based on the continued fraction expansion of the solution. In…

Functional Analysis · Mathematics 2024-04-05 Ivan Kovalyov , Stefan Kunis

The Hausdorf moment problem (HMP) over the unit interval in an $L^2$-setting is a classical example of an ill-posed inverse problem. Since various applications can be rewritten in terms of the HMP, it has gathered significant attention in…

Numerical Analysis · Mathematics 2021-05-20 Daniel Gerth , Bernd Hofmann , Christopher Hofmann , Stefan Kindermann

We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach…

Spectral Theory · Mathematics 2025-05-13 Alexander Mikhaylov , Victor Mikhaylov