Related papers: Constructive approach to the truncated moment prob…
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…
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 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…
In this paper we study the bivariate truncated moment problem (TMP) on curves of the form $y=q(x)$, $q(x)\in \mathbb{R}[x]$, $\text{deg } q\geq 3$, and $yx^\ell=1$, $\ell\in \mathbb{N}\setminus\{1\}$. For even degree sequences the solution…
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…
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…
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 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…
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.…
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}…
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.
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…
Let $\gamma^{(m)} \equiv \{ \gamma_{ij} \}_{0 \leq i +j \leq m}$ be a given complex-valued sequence. The truncated complex moment problem (TCMP in short) involves determining necessary and sufficient conditions for the existence of a…
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…
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,…
Let Q(x,y)=0 be an hyperbola in the plane. Given real numbers $\beta \equiv\beta^{2n)}=\{\beta_{ij}\}_{i,j\geq0,i+j\leq2n}$, with $\beta_{00}>0$, the truncated Q-hyperbolic moment problem for \beta entails finding necessary and sufficient…
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…
Cubic forms in three variables are parametrised by points of $\P^9$. We study the subvarieties in this space defined by decomposable forms. Specifically, we calculate the equivariant minimal resolutions of these varieties and describe their…
In this paper we study the truncated operator trigonometric moment problem. All solutions of the moment problem are described by a Nevanlinna-type parameterization. In the case of moments acting in a separable Hilbert space, the matrices of…
We propose a conic transformation method to solve the Perspective-Three-Point (P3P) problem. In contrast to the current state-of-the-art solvers, which formulate the P3P problem by intersecting two conics and constructing a degenerate conic…