Related papers: Truncated K-moment problems in several variables

Questions on random matrices and on non-intersecting Brownian motions have led to the study of moment matrices with regard to several weights. The purpose of this paper is to show that the determinants of such moment matrices satisfy, upon…

Let $\K$ be an algebraic number field of degree $d$ and discriminant $\Delta$ over $\Q$. Let $\A$ be an associative algebra over $\K$ given by structure constants such that $\A\cong M_n(\K)$ holds for some positive integer $n$. Suppose that…

Given proper cones $K_1$ and $K_2$ in $\mathbb{R}^n$ and $\mathbb{R}^m$, respectively, an $m \times n$ matrix $A$ with real entries is said to be semipositive if there exists a $x \in K_1^{\circ}$ such that $Ax \in K_2^{\circ}$, where…

Two representations of a reductive group G are spectrally equivalent if the same irreducible representations appear in both of them. The semigroup of finite dimensional representations of G with tensor product and up to spectral equivalence…

Let $G$ be a connected compact group equipped with the normalised Haar measure $\mu$. Our first result shows that given $\alpha, \beta>0$, there is a constant $c = c(\alpha,\beta)>0$ such that for any compact sets $A,B\subseteq G$ with $…

We prove the following theorem. Let $\mu$ be a measure on $R^n$ with even continuous density, and let $K,L$ be origin-symmetric convex bodies in $R^n$ so that $\mu(K\cap H)\le \mu(L\cap H)$ for any central hyperplane H. Then $\mu(K)\le…

We show that higher order inter-group covariances involving even number of qubits are necessarily positive semidefinite for N qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads…

We find a semi-algebraic description of the Minkowski sum $\mathcal{A}_{3,n}$ of $n$ copies of the bounded twisted cubic $\{(t,t^2,t^3)\mid -1\leq t\leq 1\}$ for each integer $n\geq3$. These descriptions provide efficient membership tests…

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…

In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space Hamiltonian…

(1) Let 1\leq k\leq \omega. Call an atom structure \alpha weakly k neat representable, the term algebra is in \RCA_n\cap \Nr_n\CA_{n+k}, but the complex algebra is not representable. Call an atom structure neat if there is an atomic algebra…

In this paper we study truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint and $J$-unitary operators. Conditions of the solvability are given. Some canonical solutions of the moment problems are constructed. As a…

In this paper we prove: Theorem 1. Let $\mathcal{K}$ be an abstract elementary class which satisfies the joint embedding and amalgamation properties. Suppose $\lambda>\mu\geq LS(\mathcal{K})$ and $\theta$ is a limit ordinal $<\lambda^+$. If…

We address the extension problem for quantal measures of path-integral type, concentrating on two cases: sequential growth of causal sets, and a particle moving on the finite lattice Z_n. In both cases the dynamics can be coded into 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 $K$…

We investigate parameterized multipartite entanglement measures from the perspective of $k$-nonseparability in this paper. We present two types of entanglement measures in $n$-partite systems, $q$-$k$-ME concurrence $(q\geq2,~2\leq k\leq…

We characterize the existence of the Lebesgue integrable solutions of the truncated problem of moments in several variables on unbounded supports by the existence of some maximum entropy -- type representing densities and discuss a few…

This work extends Favard-type spectral representations for banded matrices $T$ beyond the bounded setting. It assumes that, for every $N\in\mathbb N_0$, there exists a shift $s_N\ge 0$ such that the shifted truncation $A_N:= T^{[N]}+s_N…

We consider the sequence $( Q_n )_{n=1}^{\infty}$ of semi-meander polynomials which are used in the enumeration of semi-meandric systems (a family of diagrams related to the classical stamp-folding problem). We show that for a fixed natural…

In this paper we prove the existence of at least one positive solution for nonlocal semipositone problem of the type $$ (P_\lambda^\mu)\left\{ \begin{array}{lll} (-\Delta)^s u&=& \lambda(u^{q}-1)+\mu u^r \mbox{ in } \Omega\\ u&>&0 \mbox{ in…