Spectral asymptotics of non-self-adjoint elliptic systems of differential operators in bounded domains

Remarks on interior transmission eigenvalues, Weyl formula and branching billiards

“…The first statement of the theorem and the first part of the last statement (concerning σ = 1) are immediate consequences of the parameter ellipticity of the problem established in theorem 1.2. The second statement follows from theorem 1.2 and results obtained in [2], where the main term of the Weyl asymptotics is justified for non-symmetric parameter-elliptic system if the eigenvalues of the main symbol A of the system belong to R + . Formula (10) holds in this case with…”

“…dξ, which implies (11). The part of the third statement concerning the case σ = −1 is a consequence of theorem 2 from [2]. The latter theorem estimates the number of the eigenvalues of the problem in a sector, which does not contain the eigenvalues of the principle symbol of the operator.…”