On the eigenvalues of certain canonical higher-order ordinary differential operators

We consider the operator of taking the 2pth 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. © 2005 Elsevier Inc. All rights reserved