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The second weyl coefficient for a first order system

Avetisyan, Z; Sjöstrand, J; Vassiliev, D; (2020) The second weyl coefficient for a first order system. Operator Theory: Advances and Applications , 276 pp. 120-153. 10.1007/978-3-030-31531-3_10.

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Abstract

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.

Type: Article
Title: The second weyl coefficient for a first order system
DOI: 10.1007/978-3-030-31531-3_10
Publisher version: https://doi.org/10.1007/978-3-030-31531-3_10
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: spectral theory, asymptotic distribution of eigenvalues
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10107798
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