The 2-Transitive Transplantable Isospectral Drums
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The 2-Transitive Transplantable Isospectral Drums
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| Creator |
Schillewaert, J.
Thas, K. |
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| Description |
For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [Proc. Nat. Acad. Sci. USA 51 (1964), 542]; in the present paper, we investigate pairs of domains in R² which are isospectral but not congruent. All known such counter examples to M. Kac's famous question can be constructed by a certain tiling method (''transplantability'') using special linear operator groups which act 2-transitively on certain associated modules. In this paper we prove that if any operator group acts 2-transitively on the associated module, no new counter examples can occur. In fact, the main result is a corollary of a result on Schreier coset graphs of 2-transitive groups.
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| Date |
2019-02-14T17:51:03Z
2019-02-14T17:51:03Z 2011 |
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| Type |
Article
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| Identifier |
The 2-Transitive Transplantable Isospectral Drums / J. Schillewaert, K. Thas // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 20D06; 35J10; 35P05; 37J10; 58J53 DOI: http://dx.doi.org/10.3842/SIGMA.2011.080 http://dspace.nbuv.gov.ua/handle/123456789/147407 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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