Related papers: On Helson matrices: moment problems, non-negativit…
We prove that the Markov-Stieltjes transform is a bounded non compact Hankel operator on Hardy space $H^p$ with Hilbert matrix with respect to the standard Schauder basis of $H^p$ and a bounded non compact operator on Lebesgue space…
Paley's theorem about lacunary coefficients of functions in the classical space $H^1$ on the unit circle is equivalent to the statement that certain Hankel matrices define bounded operators on $\ell^2$ of the nonnegative integers. Since…
A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable if it can be written as a summation of Kronecker products of…
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…
$H^2\zProd$ denotes the Hardy space of square integrable functions analytic in each variable separately. Let $P^{\ominus}$ be the natural projection of $L^2\zProd$ onto $\z8{H^2\zProd}$. A Hankel operator with symbol $b$ is the linear…
We consider bounded Hankel operators $H_{\psi}$ acting on the Hardy space $H^2$ to $L^2\ominus H^2$ and obtain results on the Schmidt subspaces $E^+_s(H_\psi)$ of such operators defined as the kernels of $ H_{\psi}^{\ast}H_{\psi}-s^2I$…
This paper proves two theorems. The first of these simplifies and lends clarity to the previous characterizations of the invariant subspaces of $S$, the operator of multiplication by the coordinate function $z$, on…
In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces $L^{2}(\mu)$, with $\mu$ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix to the…
For a single value of $\ell$, let $f(n,\ell)$ denote the number of lattice paths that use the steps $(1,1)$, $(1,-1)$, and $(\ell,0)$, that run from $(0,0)$ to $(n,0)$, and that never run below the horizontal axis. Equivalently, $f(n,\ell)$…
Entrywise powers of matrices have been well-studied in the literature, and have recently received renewed attention in the regularization of high-dimensional correlation matrices. In this paper, we study powers of positive semidefinite…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
Motivated by the Sarason problem on the products of Hankel and Toeplitz operators on analytic function spaces, we characterize the compactness of products of block Hankel and Toeplitz operators on the vector-valued Hardy space of the unit…
Given a pair of positive real numbers $\alpha, \beta$ and a sesqui-analytic function $K$ on a bounded domain $\Omega \subset \mathbb C^m$, in this paper, we investigate the properties of the sesqui-analytic function $\mathbb K^{(\alpha,…
We study ill-conditioned positive definite matrices that are disturbed by the sum of $m$ rank-one matrices of a specific form. We provide estimates for the eigenvalues and eigenvectors. When the condition number of the initial matrix tends…
We give an explicit evaluation, in terms of products of Jacobsthal numbers, of the Hankel determinants of order a power of two for the period-doubling sequence. We also explicitly give the eigenvalues and eigenvectors of the corresponding…
We consider operators of the type $D^\alpha:H^2(\mathcal{H})\to H^2(\mathcal{H})$, where $D^\alpha$ denotes a fractional differentiation operator, and $\Gamma_\phi$ is a Hankel operator. For $\alpha>0$, we characterize boundedness in terms…
This paper discusses the left and right ranks of quaternion matrices with Hankel structure. While they are in general different for arbitrary quaternion matrices, we show that the left and right ranks of quaternion Hankel matrices are…
A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite sub-matrices of an infinite nonnegative…
We study the relation between certain non-degenerate lower Hessenberg infinite matrices $\mathcal{G}$ and the existence of sequences of orthogonal polynomials with respect to Sobolev inner products. In other words, we extend the well-known…
In this letter, we proved a matrix identity of Hankel matrices that seems unrevealed before, generated from the moments of Gaussian distributions. In particular, we derived the Cholesky decompositions of the Hankel matrices in closed-forms,…