Related papers: Logarithmic asymptotic of multi-level Hermite-Pad\…

In this work, we establish strong asymptotics of multiple orthogonal polynomials of the second type for Angelesco systems with measures that satisfy Szeg\H{o} conditions. We consider multi-indices that converge to infinity in the…

This paper presents a novel method for polynomial approximation (Hermite approximation) using the fusion of value and derivative information. Therefore, the least-squares error in both domains is simultaneously minimized. A covariance…

Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…

Below we study theoretically and numerically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic potential, its level crossing points, and its monodromy in the complex plane of its parameter. We also…

In this paper the problem is posed of determining the physically-meaningful asymptotic orderings holding for the statistical description of a large $N-$body system of hard spheres,\textit{ i.e.,} formed by $N\equiv\frac{1}{\varepsilon}…

In this paper we consider $L_{\overline{p}, \overline\alpha, \overline{\tau}}^{*}(\mathbb{T}^{m})$ anisotropic Lorentz-Zyg\-mu\-nd space $ 2\pi$ of periodic functions of $m$ variables and Nikol'skii--Besov's class $S_{\overline{p},…

We introduce and analyze some numerical results obtained by the authors experimentally. These experiments are related to the well known problem about the distribution of the zeros of Hermite--Pad\'e polynomials for a collection of three…

We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method. The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are…

For an arbitrary tuple of $m+1$ germs of analytic functions at a fixed point, we introduce the so-called polynomial Hermite-Pad\'e $m$-system (of order $n$, $n\in\mathbb N$), which consists of $m$ tuples of polynomials; these tuples, which…

We analyze the polynomials $H_{n}^{r}(x)$ considered by Gould and Hopper, which generalize the classical Hermite polynomials. We present the main properties of $H_{n}^{r}(x)$ and derive asymptotic approximations for large values of $n$ from…

We study asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight, which is a weight function with a finite number of algebraic singularities on $[-1,1]$. The recurrence coefficients…

We characterise asymptotic behaviour of families of symmetric orthonormal polynomials whose recursion coefficients satisfy certain conditions, satisfied for example by the (normalised) Hermite polynomials. More generally, these conditions…

Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex…

We discuss the notion of optimal polynomial approximants in multivariable reproducing kernel Hilbert spaces. In particular, we analyze difficulties that arise in the multivariable case which are not present in one variable, for example, a…

We fix a maximal order $\mathcal O$ in $\F=\R,\C$ or $\mathbb{H}$, and an $\F$-hermitian form $Q$ of signature $(n,1)$ with coefficients in $\mathcal O$. Let $k\in\N$. By applying a lattice point theorem on the $\F$-hyperbolic space, we…

In this paper, we present a rigorous analysis of root-exponential convergence of Hermite approximations, including projection and interpolation methods, for functions that are analytic in an infinite strip containing the real axis and…

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers $V_{\lambda}^{\otimes N}$ of an irreducible representation $V_{\lambda}$ of a compact connected Lie group $G$. The weights are…

We extend recent work of Gurel-Gurevich--Jerison--Nachmias (2020) and Bou-Rabee--Gwynne (2024) by showing that as the mesh of our lattice tends to $0$, we have a polynomial rate of convergence for the Dirichlet problem on orthodiagonal maps…

This paper is devoted to the study of general (Laurent) polynomial modifications of moment functionals on the unit circle, i.e., associated with hermitian Toeplitz matrices. We present a new approach which allows us to study polynomial…

We study asymptotic behavior of orthogonal polynomials on the unit circle with varying Verblunsky coefficients $\alpha_{n,N}$ when the ratio $n/N$ converges as $n,N\to\infty$. First, we give a streamlined proof of ratio asymptotics for…