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Spectral estimates and non-selfadjoint perturbations of spheroidal wave operators

URN to cite this document:
urn:nbn:de:bvb:355-epub-109908
DOI to cite this document:
10.5283/epub.10990
Finster, Felix ; Schmid, Harald
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Date of publication of this fulltext: 27 Nov 2009 07:03



Abstract

The spheroidal wave operator $\cal A$ is a linear elliptic operator of second order with smooth coefficients on the unit sphere $S^2$. Using angular variables $\vartheta \in (0,\pi)$ and $\phi\in [0,2\pi)$ this operator may be written in the form ${\cal A}=-{d\over{d \cos \vartheta}}\sin^2\vartheta {d\over{d \cos \vartheta}} + {1\over {\sin^2 \vartheta}}\left(\Omega\sin^2\vartheta+k\right)^2.$ ...

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