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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.
