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Felix Finster, Harald Schmid

Spectral estimates and non-selfadjoint perturbations of spheroidal wave operators

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 obtained using the theory of slightly non-selfadjoint perturbations.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 12/2006
Pages: 71 - 107

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