Transmission eigenvalues for multipoint scatterers

P. G. Grinevich; R. G. Novikov

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arXiv · 2108.08361

Transmission eigenvalues for multipoint scatterers

P. G. Grinevich·R. G. Novikov

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Abstract

We study the transmission eigenvalues for the multipoint scatterers of the Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions $d=2$ and $d=3$. We show that for these scatterers: 1) each positive energy $E$ is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex $E$ is an interior transmission eigenvalue of infinite multiplicity. The case of dimension $d=1$ is also discussed.

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P. G. Grinevich, R. G. Novikov. 2021-08-18. Transmission eigenvalues for multipoint scatterers. https://arxiv.org/abs/2108.08361

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