On a spectral theorem of Weyl
Operator Algebras
2019-08-30 v3 Classical Analysis and ODEs
Spectral Theory
Abstract
We give a geometric proof of a theorem of Weyl on the continuous part of the spectrum of Sturm-Liouville operators on the half-line with asymptotically constant coefficients. Earlier proofs due to Weyl and Kodaira depend on special features of Green's functions for linear ordinary differential operators; ours might offer better prospects for generalization to higher dimensions, as required for example in noncommutative harmonic analysis.
Keywords
Cite
@article{arxiv.1611.03396,
title = {On a spectral theorem of Weyl},
author = {Nigel Higson and Qijun Tan},
journal= {arXiv preprint arXiv:1611.03396},
year = {2019}
}
Comments
The paper has been reorganized and shortened. Some standard computations have been omitted