Heriot-Watt Mathematics Report Series
HWM01-3, 19 Feb 2001
Commutators, Spectral Trace Identities, and Universal Estimates for Eigenvalues
M Levitin and L Parnovski
Abstract
Using simple commutator relations, we obtain several trace identities
involving eigenvalues and eigenfunctions of an abstract self-adjoint
operator acting in a Hilbert space. Applications involve abstract
universal estimates for the eigenvalue gaps. As particular examples,
we present simple proofs of the classical universal estimates for
eigenvalues of the Dirichlet Laplacian (Payne-Polya-Weinberger,
Hile-Protter, etc.), as well as of some known and new results
for other differential operators and systems. We also suggest an
extension of the methods to the case of non-self-adjoint operators.
Google Scholar Search: links, citations and journal (if available)
Contact Details | 2001 Reports Index |
Full Index