Spectral estimates and non-selfadjoint perturbations of spheroidal wave operators

Zusammenfassung

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 obtained using the theory of slightly non-selfadjoint perturbations.