Michael Hitrik

Transmission Eigenvalues for Elliptic Operators

A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-self-adjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trace class case, the generic existence of transmission eigenvalues is established.

TRANSMISSION EIGENVALUES FOR OPERATORS WITH CONSTANT COEFFICIENTS

In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order

Non-Selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions I

\ge 2

Tunnel effect and symmetries for Kramers–Fokker–Planck type operators

with constant real coefficients. Under suitable growth conditions on the symbol of the operator and the perturbation, we show the discreteness of the set of transmission eigenvalues and derive sufficient conditions on the existence of transmission eigenvalues. We apply these techniques to the case of the biharmonic operator and the Dirac system. In the hypoelliptic case we present a connection to scattering theory.

Tunnel Effect for Kramers-Fokker-Planck Type Operators

Abstract. This is the first in a series of works devoted to small non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength

{\mathcal P}{\mathcal T}

\epsilon

Diophantine tori and spectral asymptotics for nonselfadjoint operators

of the perturbation is