The 2-Transitive Transplantable Isospectral Drums
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&#...
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| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147407 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The 2-Transitive Transplantable Isospectral Drums / J. Schillewaert, K. Thas // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1474072019-02-15T01:23:38Z The 2-Transitive Transplantable Isospectral Drums Schillewaert, J. Thas, K. 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. 2011 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Schillewaert, J. Thas, K. |
| spellingShingle |
Schillewaert, J. Thas, K. The 2-Transitive Transplantable Isospectral Drums Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Schillewaert, J. Thas, K. |
| author_sort |
Schillewaert, J. |
| title |
The 2-Transitive Transplantable Isospectral Drums |
| title_short |
The 2-Transitive Transplantable Isospectral Drums |
| title_full |
The 2-Transitive Transplantable Isospectral Drums |
| title_fullStr |
The 2-Transitive Transplantable Isospectral Drums |
| title_full_unstemmed |
The 2-Transitive Transplantable Isospectral Drums |
| title_sort |
2-transitive transplantable isospectral drums |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147407 |
| citation_txt |
The 2-Transitive Transplantable Isospectral Drums / J. Schillewaert, K. Thas // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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