The asymptotics for the number of eigenvalue branches for the magnetic Schrödinger operator H - ? W in a gap of H.
The density of states of a local almost periodic operator in
We prove the existence of the density of states of a local, self-adjoint operator determined by a coercive, almost periodic quadratic form on . The support of the density coincides with the spectrum of the operator in .
The distribution of eigenvalues of partial differential operators
The Leray measure of nodal sets for random eigenfunctions on the torus
We study nodal sets for typical eigenfunctions of the Laplacian on the standard torus in dimensions. Making use of the multiplicities in the spectrum of the Laplacian, we put a Gaussian measure on the eigenspaces and use it to average over the eigenspace. We consider a sequence of eigenvalues with growing multiplicity .The quantity that we study is the Leray, or microcanonical, measure of the nodal set. We show that the expected value of the Leray measure of an eigenfunction is constant, equal...
The Logarithmic Hardy-Littlewood-Sobolev Inequlity and Extremals of Zeta Functions on Sn.
The magnetic Schrödinger operator and reverse Hölder class
The Residue of the Local Eta Function at the Origin.
The Selberg trace formula for the Picard group SL(2, Z[i])
The spectral distribution of a globally elliptic operator
The Spectrum of Positive Elliptic Operators and Periodic Bicharacteristics.
The spectrum of the damped wave operator for a bounded domain in .
The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms
The theory of Markov processes and the analysis on Lie groups are used to study the eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials.
The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin
Let A be a pseudodifferential operator on whose Weyl symbol a is a strictly positive smooth function on such that for some ϱ>0 and all |α|>0, is bounded for large |α|, and . Such an operator A is essentially selfadjoint, bounded from below, and its spectrum is discrete. The remainder term in the Weyl asymptotic formula for the distribution of the eigenvalues of A is estimated. This is done by applying the method of approximate spectral projectors of Tulovskiĭ and Shubin.
Théorie spectrale d'une classe d'opérateurs différentiels hypoelliptiques
Threshold scattering in two dimensions
Trace Properties of the Dirichlet Laplacian.
Tunnel effect and symmetries for non-selfadjoint operators
We study low lying eigenvalues for non-selfadjoint semiclassical differential operators, where symmetries play an important role. In the case of the Kramers-Fokker-Planck operator, we show how the presence of certain supersymmetric and -symmetric structures leads to precise results concerning the reality and the size of the exponentially small eigenvalues in the semiclassical (here the low temperature) limit. This analysis also applies sometimes to chains of oscillators coupled to two heat baths,...
Two remarks about spectral asymptotics of pseudodifferential operators
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.