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
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We derive a spectral representation for the oblate spheroidal wave operator, which is holomorphic in the aspherical parameter formula3 in a neighborhood of the real line. For real formula3, estimates are derived for all eigenvalue gaps uniformly in formula3.

The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex formula3 is derived using the theory of slightly non-selfadjoint perturbations.

03.07.2017, 01:40