Related papers: The truncated univariate rational moment problem

Let $K$ be a non-polar compact subset of $\mathbb{R}$ and $\mu_K$ denote the equilibrium measure of $K$. Furthermore, let $P_n\left(\cdot, \mu_K\right)$ be the $n$-th monic orthogonal polynomial for $\mu_K$. It is shown that…

For the strictly positive case (the suboptimal case), given stable rational matrix functions $G$ and $K$, the set of all $H^\infty$ solutions $X$ to the Leech problem associated with $G$ and $K$, that is, $G(z)X(z)=K(z)$ and $\sup_{|z|\leq…

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…

Let $K$ be a convex body in $\mathbb{R}^n$ and $f : \partial K \rightarrow \mathbb{R}_+$ a continuous, strictly positive function with $\int\limits_{\partial K} f(x) d \mu_{\partial K}(x) = 1$. We give an upper bound for the approximation…

We call a CNF formula linear if any two clauses have at most one variable in common. Let Linear k-SAT be the problem of deciding whether a given linear k-CNF formula is satisfiable. Here, a k-CNF formula is a CNF formula in which every…

This paper is a continuation of our previous investigation on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no.6, 786-797. In the present paper we obtain a Nevanlinna-type formula for this moment problem…

We address the exact recovery of a k-sparse vector in the noiseless setting when some partial information on the support is available. This partial information takes the form of either a subset of the true support or an approximate subset…

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)…

Consider a mixing dynamical systems $([0,1], T, \mu)$, for instance a piecewise expanding interval map with a Gibbs measure $\mu$. Given a non-summable sequence $(m_k)$ of non-negative numbers, one may define $r_k (x)$ such that $\mu (B(x,…

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 dynamic minimization problems of the calculus of variations with generalized Lagrangian functionals that depend on a general linear operator $K$ and defined on bounded-time intervals. Under assumptions of regularity, convexity and…

We study compactness for nonnegative solutions of the fourth order constant $Q$-curvature equations on smooth compact Riemannian manifolds of dimension $\ge 5$. If the $Q$-curvature equals $-1$, we prove that all solutions are universally…

We consider the following class of submodular k-multiway partitioning problems: (Sub-$k$-MP) $\min \sum_{i=1}^k f(S_i): S_1 \uplus S_2 \uplus \cdots \uplus S_k = V \mbox{ and } S_i \neq \emptyset \mbox{ for all }i\in [k]$. Here $f$ is a…

In this paper, we study the problem of computing by relaxation hierarchies the infimum of a real polynomial function f on a closed basic semialgebraic set and the points where this infimum is reached, if they exist. We show that when the…

Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the…

We consider the multiple Dirichlet series associated to the $k$th moment of real Dirichlet $L$-functions, and prove that it has a meromorphic continuation to a specific region in $\mathbb{C}^{k+1}$, which is conditional under the…

$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Recently, semidefinite programming (SDP) relaxations have been proposed for solving the $K$-means optimization problem, which enjoy…

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…

For a degree 2n finite sequence of real numbers $\beta \equiv \beta^{(2n)}= \{ \beta_{00},\beta_{10}, \beta_{01},\cdots, \beta_{2n,0}, \beta_{2n-1,1},\cdots, \beta_{1,2n-1},\beta_{0,2n} \}$ to have a representing measure $\mu $, it is…

We study the ring of all functions from the positive integers to some field. This ring, which we call \emph{the ring of number-theoretic functions}, is an inverse limit of the ``truncations'' \Gamma_n consisting of all functions f for which…