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Location and Weyl Formula for the Eigenvalues of Some Non Self-Adjoint Operators

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Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics

Part of the book series: Springer INdAM Series ((SINDAMS,volume 17))

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Abstract

We present a survey of some recent results concerning the location and the Weyl formula for the complex eigenvalues of two non self-adjoint operators. We study the eigenvalues of the generator G of the contraction semigroup e tG, # t ≥ 0, related to the wave equation in an unbounded domain Ω with dissipative boundary conditions on ∂ Ω. Also one examines the interior transmission eigenvalues (ITE) in a bounded domain K obtaining a Weyl formula with remainder for the counting function N(r) of complex (ITE). The analysis is based on a semi-classical approach.

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Authors and Affiliations

  1. Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351, Cours de la Libération, 33405, Talence Cedex, France

    Vesselin Petkov

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  1. Vesselin Petkov
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Correspondence to Vesselin Petkov .

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Editors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Ferruccio Colombini

  2. Dipartimento di Matematica e Geoscienze, Università di Trieste, Trieste, Italy

    Daniele Del Santo

  3. Institut de Mathématiques de Bordeaux, Université de Bordeaux - UMR5251, Talence, France

    David Lannes

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Petkov, V. (2017). Location and Weyl Formula for the Eigenvalues of Some Non Self-Adjoint Operators. In: Colombini, F., Del Santo, D., Lannes, D. (eds) Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics. Springer INdAM Series, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-52042-1_8

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