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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
26/2004

Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

Felix Finster and Harald Schmid

Abstract

We derive a spectral representation for the oblate spheroidal wave operator, which is holomorphic in the aspherical parameter $\Omega$ in a neighborhood of the real line. For real $\Omega$, estimates are derived for all eigenvalue gaps uniformly in~$\Omega$.

The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex $\Omega$ is derived using the theory of slightly non-selfadjoint perturbations.

Received:
05.05.04
Published:
05.05.04

Related publications

inJournal
2006 Repository Open Access
Felix Finster and Harald Schmid

Spectral estimates and non-selfadjoint perturbations of spheroidal wave operators

In: Journal für die reine und angewandte Mathematik (Crelle's Journal), 601 (2006), pp. 71-107