6533b7d3fe1ef96bd1260a80
RESEARCH PRODUCT
The second Weyl coefficient for a first-order system
Dmitri VassilievJohannes SjöstrandZhirayr Avetisyansubject
Spectral theoryMathematics and Statisticsasymptotic distribution of eigenvaluesScalar (mathematics)First order systemSpectral theoryEigenvalues and eigenvectorsMathematicsMathematical physicsdescription
For a scalar elliptic self-adjoint operator on a compact manifold without boundary we have two-term asymptotics for the number of eigenvalues between 0 and λ when λ → ∞, under an additional dynamical condition. (See [3, Theorem 3.5] for an early result in this direction.) In the case of an elliptic system of first order, the existence of two-term asymptotics was also established quite early and as in the scalar case Fourier integral operators have been the crucial tool. The complete computation of the coefficient of the second term was obtained only in the 2013 paper [2]. In the present paper we simplify that calculation. The main observation is that with the existence of two-term asymptotics already established, it suffices to study the resolvent as a pseudodifferential operator in order to identify and compute the second coefficient.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-01-01 |