Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators
Felix Finster and Harald Schmid
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Submission date: 05. May. 2004
published in: Journal für die reine und angewandte Mathematik, 601 (2006), p. 71-107
DOI number (of the published article): 10.1515/CRELLE.2006.095
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We derive a spectral representation for the oblate spheroidal wave operator, which is holomorphic in the aspherical parameter in a neighborhood of the real line. For real , estimates are derived for all eigenvalue gaps uniformly in .
The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex is derived using the theory of slightly non-selfadjoint perturbations.