Related papers: Solution of the polynomial moment problem

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…

We study a class of (conservative) low regularity solutions to the Camassa-Holm equation on the line by exploiting the classical moment problem (in the framework of generalized indefinite strings) to develop the inverse spectral transform…

We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…

Polynomials related to rational solutions of Painleve' equations satisfy certain difference equations. Conditions are given to acertain that all solutions really are polynomials.

We first show the existence and nature of convergence to a limiting set of roots for polynomials in a three-term recurrence of the form $p_{n+1}(z) = Q_k(z)p_{n}(z)+ \gamma p_{n-1}(z)$ as $n$ $\rightarrow$ $\infty$, where the coefficient…

We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…

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…

We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions $H\simeq R_{0,2}$, or to the real Clifford algebra $R_{0,3}$. In the quaternionic case, the approach by means of…

A general solution for a second-order linear constant coefficient dynamic equation with polynomial forcing on time scales is given.

This short paper is concerned with polynomial Pell equations \[P^2-DQ^2=1,\] with $P,Q,D\in\Bbb C[X]$ and ${deg}(D)=2$. The main result shows that the polynomials $P$ and $Q$ are closely related to Chebyshev polynomials. We then investigate…

Classifications of irreducible components of the set of polynomial differential equations with a fixed degree and with at least one center singularity lead to some other new problems on Picard-Lefschetz theory and Brieskorn modules of…

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

In this paper, we give a quantum algorithm which solves collision problem in an expected polynomial time. Especially, when the function is two-to-one, we present a quantum algorithm which can find a collision with certainty in a worst-case…

We construct polynomial solutions modulo $p^s$ of the differential KZ and dynamical equations where $p$ is an odd prime number.

Let $\{\mathbb{P}_n\}_{n\ge 0}$ and $\{\mathbb{Q}_n\}_{n\ge 0}$ be two monic polynomial systems in several variables satisfying the linear structure relation $$\mathbb{Q}_n = \mathbb{P}_n + M_n \mathbb{P}_{n-1}, \quad n\ge 1,$$ where $M_n$…

Let $K:={x: g(x)\leq 1}$ be the compact sub-level set of some homogeneous polynomial $g$. Assume that the only knowledge about $K$ is the degree of $g$ as well as the moments of the Lebesgue measure on $K$ up to order 2d. Then the vector of…

This paper presents a novel Fourier spectral method that utilizes optimization techniques to ensure the positivity and conservation of moments in the space of trigonometric polynomials. We rigorously analyze the accuracy of the new method…

This paper presents new formulary solutions for quantic polynomial equations in general forms, where we present five solutions for any fifth degree polynomial equation with real coefficients, and thereby having the possibility to calculate…

The idea of this review article is to discuss in a unified way the orthogonality of all positive definite polynomial solutions of the $q$-hypergeometric difference equation on the $q$-linear lattice by means of a qualitative analysis of the…

We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…