P. G. Grinevich, R. G. Novikov, “Transmission eigenvalues for multipoint scatterers”, Eurasian Journal of Mathematical and Computer Applications, 2021, Volume 9, Issue 4,Pages <nobr>17

This article is cited in 1 paper

Transmission eigenvalues for multipoint scatterers

P. G. Grinevich^abc, R. G. Novikov^de

^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

Language: English

DOI: 10.32523/2306-6172-2021-9-4-17-25