| Project/Area Number |
23540251
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
IWASAKI Chisato 兵庫県立大学, 大学院・物質理学研究科, 教授 (30028261)
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| Research Collaborator |
BAUER Wolfram G¨ottingen 大学, 教授
MARKINA Irina Bergen 大学, 教授
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | sub-Laplacian / sub-Riemann 構造 / 熱核 / Spectral zeta 関数 / ベキ零多様体 / Grushin type 作用素 / Clifford 代数 / 一般ハイゼンベルグタイプ群 / sub Laplacian / sub Riemann structure / Grushin type operator / spectral zeta function / Clifford algebra / spectral zeta 関数 / zeta determinant / Grushin作用素 / ベキ零リー群 / Heisenberg 群 / Spectral zeta関数 / ベキ零Lie群 / 作用関数 / Zeta正則化行列式 / 漸近展開 |
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| Research Abstract |
(1) We proved that spectral zeta functions on compact nilmanifolds of 2 step are always analytically continued to a meromorphic function with only one simple pole, determined its location formula and gave the residue there together with the ratio by the volume being constant. Also was proved that at the negative integers the function always vanishes. (2) It was proved that among the spheres only on 3, 7 and 15 dimensional spheres, there exists a triviazilable sub-Riemannian structure, especially on 15 dimensional sphere, it was shown that it is of codimension 7. We partly determined the eigenvalues and eigenfunctions for the corresponding sub-Laplacians, including the sub-Laplacian for the codimension 3 case on 7 dimensional sphere. (3) We constructed an action function for a higher step Grushin type operator with two variables in an integral form which is a first step for the construction of the heat kernel for this operator.
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