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Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

Felix Finster·Harald Schmid
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Abstract

We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter $Ω$ in a neighborhood of the real line. For real $Ω$, estimates are derived for all eigenvalue gaps uniformly in $Ω$. The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex $Ω$ is derived using the theory of slightly non-selfadjoint perturbations.

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BibTeXRIS

Felix Finster, Harald Schmid. 2006-07-23. Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators. https://doi.org/10.1515/crelle.2006.095

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