Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

Details Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

2004-05-04

arxiv.org/abs/math-ph/0405010v4

J. Reine Angew. Math. 601 (2006) 71-107

Physics

Mathematical Physics

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

Scientific paper

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.

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