On the Integral Geometry of Liouville Billiard Tables |
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Authors: | G. Popov P. Topalov |
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Affiliation: | 1.Laboratoire de Mathématiques Jean Leray, CNRS: UMR6629,Université de Nantes,Nantes Cedex 03,France;2.Department of Mathematics,Northeastern University,Boston,USA |
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Abstract: | 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. |
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