Renormalized oscillation theory for Hamiltonian systems
Classical Analysis and ODEs
2017-04-18 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
We extend a result on renormalized oscillation theory, originally derived for Sturm-Liouville and Dirac-type operators on arbitrary intervals in the context of scalar coefficients, to the case of general Hamiltonian systems with block matrix coefficients. In particular, this contains the cases of general Sturm-Liouville and Dirac-type operators with block matrix-valued coefficients as special cases. The principal feature of these renormalized oscillation theory results consists in the fact that by replacing solutions by appropriate Wronskians of solutions, oscillation theory now applies to intervals in essential spectral gaps where traditional oscillation theory typically fails.
Cite
@article{arxiv.1608.02116,
title = {Renormalized oscillation theory for Hamiltonian systems},
author = {Fritz Gesztesy and Maxim Zinchenko},
journal= {arXiv preprint arXiv:1608.02116},
year = {2017}
}
Comments
23 pages, incorporated some updates