Browsing by Subject "multiple orthogonal polynomials"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Jacobi matrices on trees generated by Angelesco systems: Asymptotics of coefficients and essential spectrum
    (EMS, 2021) Aptekarev, Alexander I.; Denisov, Sergey A.; Yattselev, Maxim L.; Mathematical Sciences, School of Science
    We continue studying the connection between Jacobi matrices defined on a tree and multiple orthogonal polynomials (MOPs) that was recently discovered. In this paper, we consider Angelesco systems formed by two analytic weights and obtain asymptotics of the recurrence coefficients and strong asymptotics of MOPs along all directions (including the marginal ones). These results are then applied to show that the essential spectrum of the related Jacobi matrix is the union of intervals of orthogonality.
  • Thumbnail Image
    Item
    Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials
    (AMS, 2020) Aptekarev, Alexander I.; Denisov, Sergey A.; Yattselev, Maxim L.; Mathematical Sciences, School of Science
    We consider a set of measures on the real line and the corresponding system of multiple orthogonal polynomials (MOPs) of the first and second type. Under some very mild assumptions, which are satisfied by Angelesco systems, we define self-adjoint Jacobi matrices on certain rooted trees. We express their Green’s functions and the matrix elements in terms of MOPs. This provides a generalization of the well-known connection between the theory of polynomials orthogonal on the real line and Jacobi matrices on to a higher dimension. We illustrate the importance of this connection by proving ratio asymptotics for MOPs using methods of operator theory.
  • Thumbnail Image
    Item
    Strong Asymptotics of Hermite-Padé Approximants for Angelesco Systems
    (Canadian Mathematical Society, 2016-10) Yattselev, Maxim L.; Department of Mathematical Sciences, School of Science
    In this work type II Hermite-Padé approximants for a vector of Cauchy transforms of smooth Jacobi-type densities are considered. It is assumed that densities are supported on mutually disjoint intervals (an Angelesco system with complex weights). The formulae of strong asymptotics are derived for any ray sequence of multi-indices.