Related papers: Positivstellens\"atze and Moment problems with Uni…

Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we…

Recently a moment-sum-of-squares hierarchy for exit location estimation of stochastic processes has been presented. When restricting to the special case of the unit ball, we show that the solutions approach the optimal value by a…

The matrix Fej\'er-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line. In the previous work of the second-named author this was extended to the characterization on arbitrary closed semialgebraic sets $K$…

The strong truncated Hamburger moment problem (STHMP) of degree $(-2k_1,2k_2)$ asks to find necessary and sufficient conditions for the existence of a positive Borel measure, supported on $\mathbb{R}\setminus \{0\}$, such that $\beta_i=\int…

Coherent states are required to form a complete set of vectors in the Hilbert space by providing the resolution of identity. We study the completeness of coherent states for two different models in a noncommutative space associated with the…

This paper deals with the moment problem on a (not necessarily finitely generated) commutative unital real algebra $A$. We define moment functionals on $A$ as linear functionals which can be written as integrals over characters of $A$ with…

Let A be a finite subset of N^n and R[x]_A be the space of real polynomials whose monomial powers are from A. Let K be a compact basic semialgebraic set of R^n such that R[x]_A contains a polynomial that is positive on K. Denote by P_A(K)…

In K\"ahler geometry, the Donaldson-Fujiki moment map picture interprets the scalar curvature of a K\"ahler metric as a moment map on the space of compatible almost complex structures on a fixed symplectic manifold. In this paper, we…

For random matrix ensembles with unitary symmetry, there is interest in the large $N$ form of the moments of the absolute value of the characteristic polynomial for their relevance to the Riemann zeta function on the critical line, and to…

We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to…

Consider an $L^1$-continuous functional $\ell$ on the vector space of polynomials of Brownian motion at given times, suppose $\ell $ commutes with the quadratic variation in a natural sense, and consider a finite set of polynomials of…

We prove that, under some additional assumption, Putinar's Positivstellensatz holds on cylinders of type $S \times {\mathbb R}$ with $S = \{x \in {\mathbb R}^n | g_1(x) \ge 0, ..., g_s(x) \ge 0\}$ such that the quadratic module generated by…

State, trace, and moment polynomials are polynomial expressions in several operator or random variables and positive functionals on their products (states, traces or expectations). While these concepts, and in particular their positivity…

We give a non-commutative Positivstellensatz for CP^n: The (commutative) *-algebra of polynomials on the real algebraic set CP^n with the pointwise product can be realized by phase space reduction as the U(1)-invariant polynomials on…

Schm\"udgen's Theorem says that if a basic closed semialgebraic set K = {g_1 \geq 0, ..., g_s \geq 0} in R^n is compact, then any polynomial f which is strictly positive on K is in the preordering generated by the g_i's. Putinar's Theorem…

Classically, a single weight on an interval of the real line leads to moments, orthogonal polynomials and tridiagonal matrices. Appropriately deforming this weight with times t=(t_1,t_2,...), leads to the standard Toda lattice and…

We prove a Positivstellensatz for operator-valued noncommutative polynomials that are positive on matrix convex sets. Specifically, let $p$ be an operator-valued polynomial in $B(H)\otimes C<x>$ of degree at most $2d+1$, where $H$ is…

In this paper, we develop a general study of contributions at infinity of Bochner-Weitzenb\"ock-type formulas on asymptotically flat manifolds, inspired by Witten's proof of the positive mass theorem. As an application, we show that similar…

In this paper we give a complete solution of the following "polynomial moment problem" which arose about 10 years ago in connection with Poincare's center-focus problem. For a given polynomial P(z) to describe polynomials Q(z) orthogonal to…

In a 2014 paper, R.E. Curto and S. Yoo proved that a moment matrix $M(3)$ with specific harmonic polynomials as column relations admits a representing measure if and only if a condition at the level of moments holds. \ In this paper, we…