[Quand un opérateur de Hill non-autoadjoint est-il un operateur spectral de type scalaire ?]
Nous dérivons des conditions nécessaires et suffisantes pour qur l'opérateur de Schrödinger (i.e., l'opérateur de Hill) dans soit un opérateur spectral de type scalaire. Les conditions montrent que cette propriétés ne dépend pas des propriétés différentielles (ou analytiques) du potentiel V.
We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator in 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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@article{CRMATH_2006__343_4_239_0,
author = {Gesztesy, Fritz and Tkachenko, Vadim},
title = {When is a non-self-adjoint {Hill} operator a spectral operator of scalar type?},
journal = {Comptes Rendus. Math\'ematique},
pages = {239--242},
publisher = {Elsevier},
volume = {343},
number = {4},
year = {2006},
doi = {10.1016/j.crma.2006.06.014},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.06.014/}
}
TY - JOUR AU - Gesztesy, Fritz AU - Tkachenko, Vadim TI - When is a non-self-adjoint Hill operator a spectral operator of scalar type? JO - Comptes Rendus. Mathématique PY - 2006 SP - 239 EP - 242 VL - 343 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.06.014/ DO - 10.1016/j.crma.2006.06.014 LA - en ID - CRMATH_2006__343_4_239_0 ER -
%0 Journal Article %A Gesztesy, Fritz %A Tkachenko, Vadim %T When is a non-self-adjoint Hill operator a spectral operator of scalar type? %J Comptes Rendus. Mathématique %D 2006 %P 239-242 %V 343 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.06.014/ %R 10.1016/j.crma.2006.06.014 %G en %F CRMATH_2006__343_4_239_0
Gesztesy, Fritz; Tkachenko, Vadim. When is a non-self-adjoint Hill operator a spectral operator of scalar type?. Comptes Rendus. Mathématique, Tome 343 (2006) no. 4, pp. 239-242. doi : 10.1016/j.crma.2006.06.014. http://www.numdam.org/articles/10.1016/j.crma.2006.06.014/
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