On the spectral theory of pseudo-differential elliptic boundary problems
Gerd Grubb (1983)
Banach Center Publications
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Gerd Grubb (1983)
Banach Center Publications
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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.
Ari Laptev, Yu Safarov (1991)
Journées équations aux dérivées partielles
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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.
Victor Ivrii (1991-1992)
Séminaire Équations aux dérivées partielles (Polytechnique)
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G. Grubb (1983-1984)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Lech Zielinski (2002)
Colloquium Mathematicae
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We describe the asymptotic distribution of eigenvalues of self-adjoint elliptic differential operators, assuming that the first-order derivatives of the coefficients are Lipschitz continuous. We consider the asymptotic formula of Hörmander's type for the spectral function of pseudodifferential operators obtained via a regularization procedure of non-smooth coefficients.
V. Ivrii (1990-1991)
Séminaire Équations aux dérivées partielles (Polytechnique)
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C. Fefferman, D. H. Phong (1980-1981)
Séminaire Équations aux dérivées partielles (Polytechnique)
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