Non-Scattering Energies and Transmission Eigenvalues in Hn

Show full item record



Permalink

http://hdl.handle.net/10138/313197

Citation

Blåsten , E & Vesalainen , E V 2020 , ' Non-Scattering Energies and Transmission Eigenvalues in Hn ' , Annales Academiae Scientiarum Fennicae. Mathematica , vol. 45 , no. 1 , pp. 547-576 . https://doi.org/10.5186/aasfm.2020.4522

Title: Non-Scattering Energies and Transmission Eigenvalues in Hn
Author: Blåsten, Emilia; Vesalainen, Esa V.
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2020
Language: eng
Number of pages: 30
Belongs to series: Annales Academiae Scientiarum Fennicae. Mathematica
ISSN: 1239-629X
URI: http://hdl.handle.net/10138/313197
Abstract: We consider non-scattering energies and transmission eigenvalues of compactly supported potentials in the hyperbolic spaces H-n. We prove that in H-2 a corner bounded by two hyperbolic lines intersecting at an angle smaller than 180 degrees always scatters, and that one of the lines may be replaced by a horocycle. In higher dimensions, we obtain similar results for corners bounded by hyperbolic hyperplanes intersecting each other pairwise orthogonally, and that one of the hyperplanes may be replaced by a horosphere. The corner scattering results are contrasted by proving discreteness and existence results for the related transmission eigenvalue problems.
Subject: ACOUSTIC-WAVES
CORNERS
FAR-FIELD PATTERNS
Hyperbolic geometry
SPHERICALLY SYMMETRICAL SPEED
THEOREMS
UNIQUE CONTINUATION
corner
interior transmission problem
non-scattering
111 Mathematics
Rights:


Files in this item

Total number of downloads: Loading...

Files Size Format View
vol45pp0547_0576.pdf 635.9Kb PDF View/Open

This item appears in the following Collection(s)

Show full item record