Study of the Analysis on Manifolds

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400124
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokyo University of Science
• Principal Investigator: Furutani Kenro 東京理科大学, 理工学部数学科, 教授 (70112901)
• Co-Investigator(Renkei-kenkyūsha): Iwasaki Chisato 兵庫県立大学, 物質理学研究科, 特命教授 (30028261) ; Tamura Mitsuji 東京理科大学, 理工学部, 助教 (60536548)
• Research Collaborator: Bauer Wolfram ハノーバ大学, 教授 ; Markina Irina ベルゲン大学, 教授 ; Vasiliev Alexander ベルゲン大学, 教授 ; Tamura Mitsuji
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 関数解析学 / 大域解析学 / non-holonomic structure / 劣楕円型作用素 / Grushin type operator / spectral zeta function / heat kernel / 国際共同研究

Outline of Final Research Achievements

(1) We proved the existence of integral lattices in the Lie groups attached to Clifford algebras and their admissible modules and classified them corresponding to minimal admissible modules. Also we studied the spectral zeta function of the sub-Laplacians on some of their Lie groups and their compact quotients by lattices which we proved the existence. (2) We constructed Green kernels for higher step Grushin operators coming from sub-Laplacians on higher step nilpotent Lie groups (Carnot groups) by two different methods. (3) A relation of the homogeneous first integrals of a sub-Laplacian and the related Grushin type operator through a submersion was proved in the framework of the pseudo-differential operator theory. (4) We constructed a codimension 3 sub-Riemannian structure on the Gromoll-Meyer exotic 7 sphere.

Free Research Field

数学