On the Eigenvalues of Certain Canonical Higher-Order Ordinary Differential Operators

Albrecht Boettcher; Harold Widom

paper

On the Eigenvalues of Certain Canonical Higher-Order Ordinary Differential Operators

arXiv:math/0501116

Abstract

We consider the operator of taking the $2 p$ th derivative of a function with zero boundary conditions for the function and its first $p - 1$ derivatives at two distinct points. Our main result provides an asymptotic formula for the eigenvalues and resolves a question on the appearance of certain regular numbers in the eigenvalue sequences for $p = 1$ and $p = 3$ .

LaTeX, 12 pages, 2 figures