When is a non-self-adjoint Hill operator a spectral operator of scalar type?
Spectral Theory
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We derive necessary and sufficient conditions for a one-dimensional periodic Schr\"odinger (i.e., Hill) operator H=-d^2/dx^2+V in L^2(R) to be a spectral operator of scalar type. The conditions demonstrate the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V.
Keywords
Cite
@article{arxiv.math/0511370,
title = {When is a non-self-adjoint Hill operator a spectral operator of scalar type?},
author = {Fritz Gesztesy and Vadim Tkachenko},
journal= {arXiv preprint arXiv:math/0511370},
year = {2007}
}
Comments
5 pages