On polynomial eigenfunctions for a class of differential operators

DOI10.4310/MRL.2002.v9.n2.a3zbMath1016.34083MaRDI QIDQ699271

Hans Rullgård, Tanja Bergkvist

Publication date: 23 July 2003

Published in: Mathematical Research Letters (Search for Journal in Brave)

zbMATH Keywords

differential operatorszeros of eigenfunctionspolynomial eigenfunction

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General theory of ordinary differential operators (47E05) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Polynomials and rational functions of one complex variable (30C10) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30)

Related Items (22)

Asymptotic distribution of zeros of a certain class of hypergeometric polynomials ⋮ On the existence of short trajectories of quadratic differentials related to generalized Jacobi polynomials with non-real varying parameters ⋮ Critical measures for vector energy: global structure of trajectories of quadratic differentials ⋮ Subharmonic Configurations and Algebraic Cauchy Transforms of Probability Measures ⋮ Zero distribution for Angelesco Hermite–Padé polynomials ⋮ Root-counting Measures of Jacobi Polynomials and Topological Types and Critical Geodesics of Related Quadratic Differentials ⋮ A refinement for rational functions of Pólya's method to construct Voronoi diagrams ⋮ On a class of equilibrium problems in the real axis ⋮ An asymptotic expansion of eigenpolynomials for a class of linear differential operators ⋮ Corrigendum: ``Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions ⋮ Choquet order for spectra of higher Lamé operators and orthogonal polynomials ⋮ Trajectories of a Quadratic Differential Related to a Particular Algebraic Equation ⋮ Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials ⋮ On spectral polynomials of the Heun equation. II ⋮ On higher Heine-Stieltjes polynomials ⋮ On asymptotics of polynomial eigenfunctions for exactly solvable differential operators ⋮ S-curves in polynomial external fields ⋮ Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions ⋮ Critical graph of a polynomial quadratic differential related to a Schrödinger equation with quartic potential ⋮ Inverse spectral problem for normal matrices and the Gauss-Lucas theorem ⋮ Distribution of critical points of polynomials ⋮ On existence of quasi-Strebel structures for meromorphic \(k\)-differentials

This page was built for publication: On polynomial eigenfunctions for a class of differential operators