Related papers: The operator approach to the truncated multidimens…
In this paper, we investigate moment methods from a general point of view using an operator notation. This theoretical approach lets us explore the moment closure problem in more detail. This gives rise to a new idea, proposed in…
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…
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 paper we consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. We compute the dimension of the space of all such operators. We also describe the matrix representations of asymmetric…
In this paper we analyze iterations of the obstacle problem for two different operators. We solve iteratively the obstacle problem from above or below for two different differential operators with obstacles given by the previous functions…
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…
The realizability problem is a well-known problem in the analysis of complex systems, which can be modeled as an infinite-dimensional moment problem. More precisely, as a truncated $K-$moment problem where $K$ is the space of all possible…
In this paper, we develop a constructive solution for the pure truncated moment problem on cubic curves in Weierstrass form, establishing the existence of a representing measure whose number of atoms equals the rank of the associated moment…
The generalized problem of moments is a conic linear optimization problem over the convex cone of positive Borel measures with given support. It has a large variety of applications, including global optimization of polynomials and rational…
The two-dimensional moment problem consists of finding a positive Borel measure $\mu$ in $\mathbb{R}^2$ such that $\int_{\mathbb{R}^2} t_1^m t_2^n d\mu = s_{m,n}$, $m,n=0,1,2,...$, where $s_{m,n}$ are prescribed real constants (moments). We…
We are concerned with the tensor equations whose coefficient tensor is an M-tensor. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
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…
In this paper we obtain a Nevanlinna-type parametrization for the operator Hamburger moment problem. The moment problem is not supposed to be necessarily completely indeterminate. No assumptions besides the solvability of the moment problem…
In this work we propose a generalization of the Moment Guided Monte Carlo method developed in [11]. This approach permits to reduce the variance of the particle methods through a matching with a set of suitable macroscopic moment equations.…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
The classical Minkowski problem for convex bodies has deeply influenced the development of differential geometry. During the past several decades, abundant mathematical theories have been developed for studying the solutions of the…
The Fourier operator truncated on a finite symmetric interval is considered. The limiting behavior of its spectrum is discussed as the length of the interval tends to infinity.
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…
The (classical) truncated moment problem, extensively studied by Curto and Fialkow, asks to characterize when a finite sequence of real numbers indexes by words in commuting variables can be represented with moments of a positive Borel…