| Project/Area Number |
26400150
|
|---|
| 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 |
Kaneko Hiroshi 東京理科大学, 理学部第一部数学科, 教授 (90194919)
|
|---|
| Project Period (FY) |
2014-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2017: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2016: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
|---|
| Keywords | マルコフ過程 / 木（ツリー） / 超距離空間 / 関数空間 / 容量 / 統計的推論 / 擬似乱数 / 固有関数 / 木構造 / 階層構造 / 理想境界 / 非アルキメデス的距離 / ディリクレ空間 |
|---|
| Outline of Final Research Achievements |
This project began with taking advantage of stochastic counterpart of the Bessel kernels and a framework on Sobolev-Orlicz capacity on ends of a tree has been invented so that capacitary estimates are derived from a spectral analytical classification of eigenfunctions according to design of tree. In second, a modified Van der Corput sequence in the ring of p-adic integers has been introduced so as to be a counterpart of Weyl’s irrational rotation on the unit interval. On the ring, a similar random Weyl sampling to the one by Sugita and Takanobu is also newly built. In third, Ben Amor’s result which had shown an important relationship of Orlicz norm with a capacitary estimate was focused on. As a result, capacitary estimates for fundamental subsets in the ends of a tree have been found in terms of a Radon measure, where a canonical orthonormal basis in the family of square integrable functions can be freed from the orthogonality determined by Dirichlet form in existing formalisms.
|
