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This article is cited in 1 scientific paper (total in 1 paper)
Transmission eigenvalues for multipoint scatterers
P. G. Grinevichabc, R. G. Novikovde
a Steklov Mathematical Institute of RAS, 8 Gubkina St. Moscow, 119991, Russia
b Landau Institute of Theoretical Physics, pr. Akademika Semenova 1a, Chernogolovka, Moscow region, 142432, Russia
c Moscow State University, Leniskie gory, Moscow, Russia
d CMAP, CNRS, École Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
e IEPT RAS, Moscow, Russia
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.
Keywords:
Schrödinger equation, transparency, transmission eigenvalues, multipoint scatterers.
Received: 16.10.2021
Revised: 19.11.2021
Accepted: 19.11.2021
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