Related papers: On bounded complex Jacobi matrices and related mom…
This paper is about the general truncated matrix-valued moment problem. Let $\mathcal{H}_q$ denote the complex Hermitian $q\times q$-matrices, $q\in \mathbb{N}$. Suppose that $(\mathcal{X},\mathfrak{X})$ is a measurable space and…
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…
We study the orthogonal polynomials associated with the equilibrium measure, in logarithmic potential theory, living on the attractor of an Iterated Function System. We construct sequences of discrete measures, that converge weakly to the…
The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher…
We consider a periodic Jacobi operator $H$ with finitely supported perturbations on ${\Bbb Z}.$ We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data: the inverse of…
Let $\{\hat{P}_{n}(x)\}$ be an orthonormal polynomial sequence and denote by $\{w_{n}(x)\}$ the respective sequence of functions of the second kind. Suppose the Hamburger moment problem for $\{\hat{P}_{n}(x)\}$ is determinate and denote by…
We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…
We investigate when a linear functional $L$ defined on a linear subspace $B$ of a unital commutative real algebra $A$ admits an integral representation w.r.t. a positive Radon measure supported on a closed subset $K$ of the character space…
Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range or exponentially decaying perturbation of a periodic Jacobi operator. As a corollary we can fully solve the inverse resonance…
We study resonances for Jacobi operators on the half lattice with matrix valued coefficient and finitely supported perturbations. We describe a forbidden domain, the geometry of resonances and their asymptotics when the main coefficient of…
We address the computational spectral theory of Jacobi operators that are compact perturbations of the free Jacobi operator via the asymptotic properties of a connection coefficient matrix. In particular, for finite-rank perturbation we…
A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing…
In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we…
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…
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…
We derive special representation for Weyl functions for finite and semi-infinite Jacobi matrices with bounded entries based on a relationship between spectral problem for Jacobi matrices and initial-boundary value problem for auxiliary…
Let $\mu$ be a positive Borel measure on the real line and let $L$ be the linear functional on univariate polynomials of bounded degree, defined as integration with respect to $\mu$. In 2020, Blekherman et al., the characterization of all…
In this paper we study Devinatz's moment problem: to find a non-negative Borel measure $\mu$ in a strip $\Pi = \{(x,\phi):\ x\in \mathbb{R},\ -\pi\leq \phi < \pi\},$ such that $\int_\Pi x^m e^{in\phi} d\mu = s_{m,n}$, $m\in \mathbb{Z}_+$,…
Let $A_j,B_j$ $(j=0,1,\ldots)$ be $m \times m$ matrices, whose elements are complex numbers, $A_j$ are selfadjoint matrices and $B_j^{-1}$ exist. We study the deficiency index problem for minimal closed symmetric operator $L$ with domain…
This paper introduces a framework to study discrete optimization problems which are parametric in the following sense: their constraint matrices correspond to matrices over the ring $\mathbb{Z}[x]$ of polynomials in one variable. We…