On the Integral Geometry of Liouville Billiard Tables

The notion of a Radon transform is introduced for completely integrable billiard tables. In the case of Liouville billiard tables of dimension 3 we prove that the Radon transform is one-to-one on the space of continuous functions K on the boundary which are invariant with respect to the correspondin...

Full description

Saved in:
Bibliographic Details
Published in:Communications in mathematical physics 2011-05, Vol.303 (3), p.721-759
Main Authors: Popov, G., Topalov, P.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical analysis
Mathematical and Computational Physics
Mathematical methods in physics
Mathematical Physics
Mathematics
Other topics in mathematical methods in physics
Physics
Physics and Astronomy
Quantum Physics
Real functions
Relativity Theory
Sciences and techniques of general use
Theoretical
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The notion of a Radon transform is introduced for completely integrable billiard tables. In the case of Liouville billiard tables of dimension 3 we prove that the Radon transform is one-to-one on the space of continuous functions K on the boundary which are invariant with respect to the corresponding group of symmetries. We prove also that the frequency map associated with a class of Liouville billiard tables is non-degenerate. This allows us to obtain spectral rigidity of the corresponding Laplace-Beltrami operator with Robin boundary conditions.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-011-1223-z