Preprint 26/2004
Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators
Felix Finster and Harald Schmid
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Submission date: 05. May. 2004
Pages: 33
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
Bibtex
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Abstract:
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.