Comptes Rendus
Ordinary Differential Equations
When is a non-self-adjoint Hill operator a spectral operator of scalar type?
Comptes Rendus. Mathématique, Volume 343 (2006) no. 4, pp. 239-242.

We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator H=d2/dx2+V in L2(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.

Nous dérivons des conditions nécessaires et suffisantes pour qur l'opérateur de Schrödinger (i.e., l'opérateur de Hill) H=d2/dx2+V dans L2(R) soit un opérateur spectral de type scalaire. Les conditions montrent que cette propriétés ne dépend pas des propriétés différentielles (ou analytiques) du potentiel V.

Published online:
DOI: 10.1016/j.crma.2006.06.014

Fritz Gesztesy 1; Vadim Tkachenko 2

1 Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
2 Department of Mathematics, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel
     author = {Fritz Gesztesy and Vadim Tkachenko},
     title = {When is a non-self-adjoint {Hill} operator a spectral operator of scalar type?},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {239--242},
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Fritz Gesztesy; Vadim Tkachenko. When is a non-self-adjoint Hill operator a spectral operator of scalar type?. Comptes Rendus. Mathématique, Volume 343 (2006) no. 4, pp. 239-242. doi : 10.1016/j.crma.2006.06.014.

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