2003 Fiscal Year Final Research Report Summary
Spectra and Geometric structure of manifolds and graph
| Project/Area Number |
14540081
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | OKAYAMA UNIVERSITY |
|---|
Principal Investigator |
KATSUDA Atsushi OKAYAMA UNIVERSITY, Faculty of Science, Associate Professor, 理学部, 助教授 (60183779)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SHIMAKAWA Kazuhisa OKAYAMA UNIVERSITY, Faculty of Science, Professor, 理学部, 教授 (70109081)
TAMURA Hideo OKAYAMA UNIVERSITY, Faculty of Science, Professor, 理学部, 教授 (30022734)
SAKAI Takashi OKAYAMA UNIVERSITY, Faculty of Science, Professor, 理学部, 教授 (70005809)
IKEDA Akira OKAYAMA UNIVERSITY, Faculty of Education, Professor, 教育学部, 教授 (30093363)
TANAKA Naoki OKAYAMA UNIVERSITY, Faculty of Science, Associate Professor, 理学部, 助教授 (00207119)
|
|---|
| Project Period (FY) |
2002 – 2003
|
| Keywords | random walk / heat kernel / nilpotent / inverse problem / spectre |
|---|
| Research Abstract |
We investigated the asymptotics of the heat kernels on covering spaces. Our results gives an extent on of the results for abelian coverings. Some point of roof is also extension in the sense that the related operators can be decomposed using representation, theory. However we need to overcome several difficult points as follows. Since the discrete nilpotent group is not type I, there is no available re resentation theory. We embed it into the Lie group and use its representation theory. However there still remain difficulties to treat infinite dimensional representations in the irreducible decomposition. Next we connect the above with decomposition of operators through the iterated integrals. Then we use semi-classical analysis and deduce the finite dimensional "decomposition" in some sense. We have also done the preparation for more detailed asymptotic expansion and an extension to solvable group case.
Others investigate the followings projects except for collaborating the above ; Geometric inequalities(Sakai), Scattering theory under magnetic fields(Tamura), Isospectral manifolds(Ikeda), Nonlinear semigroup(Tanaka), Topology of configuration spaces(Shimakawa), Cut locus on ellipsoid(Kiyohara), Completeness of TopologicalSpaces(Yoshioka), p-Laplacians(Takeuchi).
|
Research Products
(8 results)
