Related papers: Moment problem for algebras generated by a nuclear…

In this work we investigate and characterize linear functionals $L:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}$ with absolutely continuous representing measures $\mu$, i.e., $\mathrm{d}\mu(x) = g(x)\,\mathrm{d} x$ for some density $g$. We focus…

We investigate the moment problem and Jacobi matrix associated -- by the operator theoretic framework of the semilocal trace formula -- to each finite set $S$ of places of $\mathbb Q$ containing the archimedean place. The measure is given…

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…

We address some usually overlooked issues concerning the use of $*$-algebras in quantum theory and their physical interpretation. If $\mathfrak{A}$ is a $*$-algebra describing a quantum system and $\omega\colon\mathfrak{A}\to\mathbb{C}$ a…

We continue the study of truncated matrix-valued moment problems begun in arXiv:2310.00957. Let $q\in\mathbb{N}$. Suppose that $(\mathcal{X},\mathfrak{X})$ is a measurable space and $\mathcal{E}$ is a finite-dimensional vector space of…

A light-front treatment for the scalar and vector meson momentum distribution functions is developed using a model in which the nucleus is treated a static source of radius $R$. The limit $R\to \infty$ corresponds to infinite nuclear…

We employ positivity of Riesz functionals to establish representing measures (or approximate representing measures) for truncated multivariate moment sequences. For a truncated moment sequence $y$, we show that $y$ lies in the closure of…

This paper concerns positive solutions to the boundary value problems of the scalar field equation in the half space with a Sobolev supercritical nonlinearity and an inhomogeneous Dirichlet boundary condition, admitting a nontrivial…

The classical Truncated Moment problem asks for necessary and sufficient conditions so that a linear functional $L$ on $\mathcal{P}_{d}$, the vector space of real $n$-variable polynomials of degree at most $d$, can be written as integration…

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…

We develop a new framework of relative algebroids to address existence and classification problems of geometric structures subject to partial differential equations.

Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this…

We introduce the symmetric-Radon-Nikod\'ym property (sRN property) for finitely generated s-tensor norms $\beta$ of order $n$ and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if $\beta$ is a projective…

After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket…

This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their positivity and optimization over probability measures supported…

We consider the problem of finding a (non-negative) measure $\mu$ on $\mathfrak{B}(\mathbb{C}^n)$ such that $\int_{\mathbb{C}^n} \mathbf{z}^{\mathbf{k}} d\mu(\mathbf{z}) = s_{\mathbf{k}}$, $\forall \mathbf{k}\in\mathcal{K}$. Here…

In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…

For an ideal $I\subseteq\mathbb{R}[x]$ given by a set of generators, a new semidefinite characterization of its real radical $I(V_\mathbb{R}(I))$ is presented, provided it is zero-dimensional (even if $I$ is not). Moreover we propose an…

The "problem of time" in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states -- and local observables on this Hilbert space -- for a theory in which the spacetime metric is treated…

Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…