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Johannes Sjöstrand (2007-2008)
Séminaire Équations aux dérivées partielles
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We study the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random multiplicative perturbations in arbitrary dimension. We were led to quite essential improvements of many of the probabilistic aspects.
Johannes Sjöstrand (2010)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact manifolds
Dostanić, Milutin R. (1999)
Matematichki Vesnik
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Veliev, O.A. (2009)
Abstract and Applied Analysis
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William Bordeaux Montrieux, Johannes Sjöstrand (2010)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this paper, we consider elliptic differential operators on compact manifolds with a random perturbation in the 0th order term and show under fairly weak additional assumptions that the large eigenvalues almost surely distribute according to the Weyl law, well-known in the self-adjoint case.
Michele Correggi (2008-2009)
Séminaire Équations aux dérivées partielles
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We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.