Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

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.

33 pages, LaTeX, 3 figures, typo in Lemma 4.1 corrected (published version)

References in corpus (1)

• An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

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