English

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.

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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