A Spectral Representation for Spin-Weighted Spheroidal Wave Operators with Complex Aspherical Parameter
Mathematical Physics
2016-03-14 v3 General Relativity and Quantum Cosmology
Classical Analysis and ODEs
math.MP
Spectral Theory
Abstract
A family of spectral decompositions of the spin-weighted spheroidal wave operator is constructed for complex aspherical parameters with bounded imaginary part. As the operator is not symmetric, its spectrum is complex and Jordan chains may appear. We prove uniform upper bounds for the length of the Jordan chains and the norms of the idempotent operators mapping onto the invariant subspaces. The completeness of the spectral decomposition is proven.
Cite
@article{arxiv.1507.05756,
title = {A Spectral Representation for Spin-Weighted Spheroidal Wave Operators with Complex Aspherical Parameter},
author = {Felix Finster and Joel Smoller},
journal= {arXiv preprint arXiv:1507.05756},
year = {2016}
}
Comments
82 pages, LaTeX, 8 figures, minor improvements (published version)