From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation

David Krejcirik; Tereza Kurimaiova

doi:10.1007/s00020-020-02607-3

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arXiv · 2008.05176

From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation

David Krejcirik·Tereza Kurimaiova

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Abstract

Using a correspondence between the spectrum of the damped wave equation and non-self-adjoint Schroedinger operators, we derive various bounds on complex eigenvalues of the former. In particular, we establish a sharp result that the one-dimensional damped wave operator is similar to the undamped one provided that the L^1 norm of the (possibly complex-valued) damping is less than 2. It follows that these small dampings are spectrally undetectable.

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BibTeX RIS

David Krejcirik, Tereza Kurimaiova. 2020-08-12. From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation. https://doi.org/10.1007/s00020-020-02607-3

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