Transmission eigenvalues for multipoint scatterers
P.G. Grinevich (1,2,3), R.G. Novikov (4) ((1) Steklov Mathematical, Institute of Russian Academy of Sciences, Moscow, Russia, (2) L.D. Landau, Institute for Theoretical Physics, Chernogolovka, Russia, (3) Lomonosov, Moscow State University, Moscow, Russia, (4) CMAP, CNRS
TL;DR
This paper investigates transmission eigenvalues for multipoint scatterers in two and three dimensions, revealing that positive and complex energies serve as eigenvalues with infinite multiplicity, extending the understanding of scattering phenomena.
Contribution
It provides a detailed analysis of transmission eigenvalues for multipoint scatterers, showing their infinite multiplicity for positive and complex energies in higher dimensions.
Findings
Positive energies are transmission eigenvalues of infinite multiplicity.
Complex energies are interior transmission eigenvalues of infinite multiplicity.
Results extend to the case of one dimension.
Abstract
We study the transmission eigenvalues for the multipoint scatterers of the Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions and . We show that for these scatterers: 1) each positive energy is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex is an interior transmission eigenvalue of infinite multiplicity. The case of dimension is also discussed.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Geometry and complex manifolds · Advanced Mathematical Physics Problems