Eigenvalues and eigenfunctions of ordinary differential operators

On the Approximation of Isolated Eigenvalues of Ordinary Differential Operators

We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm–Liouville and Dirac operators by the eigenvalues of regular operators.

Monomiality Principle and Eigenfunctions of Differential Operators

Computing eigenvalues of ordinary differential equations

Discretisations of differential eigenvalue problems have a sensitivity to perturbations which is asymptotically least as h→ 0 when the differential equation is in first order system form. Both second and fourth order accurate discretisations of the first order system are straightforward to derive and lead to generalised eigenvalue problems of the form (A(h)− λB(h))v = 0 , where both A and B are...

Spectrality of Ordinary Differential Operators

We prove the long standing conjecture in the theory of two-point boundary value problems that completeness and Dunford’s spectrality imply Birkhoff regularity. In addition we establish the even order part of S.G.Krein’s conjecture that dissipative differential operators are Birkhoff-regular and give sharp estimate of the norms of spectral projectors in the odd case. Considerations are based on ...

Eigenvalues and Eigenfunctions

The article describes the eigenvalue and eigenfunction problems. Basic properties, some applications and examples in system analysis are provided.