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Journal of Operator Theory

Volume 70, Issue 2, Autumn 2013  pp. 437-450.

$C^*$-algebras associated with some second order differential operators

Authors E.B. Davies (1) and V. Georgescu (2)
Author institution: (1) Department of Mathematics, King's College London, Strand, London, SE21 7BS, U.K.
(2) CNRS (UMR 8088) et Departement de Mathematiques, Universite de Cergy-Pontoise, 95000 Cergy-Pontoise, France

Summary:  We compare two $C^*$-algebras that have been used to study the essential spectrum. This is done by considering a simple second order elliptic differential operator acting in $L^2(\R^N)$, which is affiliated with one or both of the algebras depending on the behaviour of the coefficients.

Keywords:  spectral analysis, essential spectrum, $C^*$-algebra, elliptic differential operator

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