The eigenvalues of hypoelliptic operators
A. Menikoff, Johannes Sjöstrand (1977)
Journées équations aux dérivées partielles
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A. Menikoff, Johannes Sjöstrand (1977)
Journées équations aux dérivées partielles
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Niels Joergen Kokholm (1989)
Journées équations aux dérivées partielles
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Johannes Sjöstrand (1980)
Annales de l'institut Fourier
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Let be a selfadjoint classical pseudo-differential operator of order with non-negative principal symbol on a compact manifold. We assume that is hypoelliptic with loss of one derivative and semibounded from below. Then exp, , is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of is computed. This paper is a continuation of a series of joint works with A. Menikoff.
V. Ivrii (1990-1991)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Everitt, W.N., Marletta, M., Zettl, A. (2001)
Journal of Inequalities and Applications [electronic only]
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Wojciech Czaja, Ziemowit Rzeszotnik (1999)
Colloquium Mathematicae
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In this paper we show an asymptotic formula for the number of eigenvalues of a pseudodifferential operator. As a corollary we obtain a generalization of the result by Shubin and Tulovskiĭ about the Weyl asymptotic formula. We also consider a version of the Weyl formula for the quasi-classical asymptotics.
O. A. Olejnik (1989)
Journées équations aux dérivées partielles
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Pushnitski, Alexander, Rozenblum, Grigori (2007)
Documenta Mathematica
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