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The 2-Transitive Transplantable Isospectral Drums
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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The 2-Transitive Transplantable Isospectral Drums
Інший ID:
2010 Mathematics Subject Classification: 20D06; 35J10; 35P05; 37J10; 58J53
DOI: http://dx.doi.org/10.3842/SIGMA.2011.080
DOI: http://dx.doi.org/10.3842/SIGMA.2011.080
Посилання:
The 2-Transitive Transplantable Isospectral Drums / J. Schillewaert, K. Thas // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ.
Підтримка:
The second author is partially supported by the Fund for Scientific Research – Flanders (Belgium).
Дата:
2011
Переглядів:
545
Завантажень:
266
Анотація:
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.
