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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147407 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The 2-Transitive Transplantable Isospectral Drums / J. Schillewaert, K. Thas // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862575209246097408 |
|---|---|
| author | Schillewaert, J. Thas, K. |
| author_facet | Schillewaert, J. Thas, K. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-11-26T11:50:03Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147407 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T11:50:03Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Schillewaert, J. Thas, K. 2019-02-14T17:51:03Z 2019-02-14T17:51:03Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/147407 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. The second author is partially supported by the Fund for Scientific Research – Flanders (Belgium). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The 2-Transitive Transplantable Isospectral Drums Article published earlier |
| spellingShingle | The 2-Transitive Transplantable Isospectral Drums Schillewaert, J. Thas, K. |
| title | 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_short | The 2-Transitive Transplantable Isospectral Drums |
| title_sort | 2-transitive transplantable isospectral drums |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147407 |
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