# Spectral estimates and non-selfadjoint perturbations of spheroidal wave operators

Finster, Felix and Schmid, Harald (2006) Spectral estimates and non-selfadjoint perturbations of spheroidal wave operators. Journal für die reine und angewandte Mathematik 601, pp. 71-107.

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## Abstract

The spheroidal wave operator is a linear elliptic operator of second order with smooth coefficients on the unit sphere . Using angular variables and this operator may be written in the form Here is the aspherical parameter. The authors consider the operator in the Hilbert space with boundary conditions It is proved that the spectral representation for 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.

Item Type:Article
Institutions: Mathematics > Prof. Dr. Felix Finster
Identification Number:
ValueType
arXiv:math-ph/0405010v4arXiv ID
Subjects:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Owner:Petra Gürster
Deposited On:27 Nov 2009 08:03
Item ID:10990
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