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2016 Fiscal Year Final Research Report

Relation between algebra, geometry and analysis on fractals

Research Project

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Project/Area Number 26287017
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKyoto University

Principal Investigator

Kigami Jun  京都大学, 情報学研究科, 教授 (90202035)

Co-Investigator(Kenkyū-buntansha) 相川 弘明  北海道大学, 理学(系)研究科(研究院), 教授 (20137889)
桑田 和正  東京工業大学, 理工学研究科, 准教授 (30432032)
日野 正訓  大阪大学, 基礎工学研究科, 教授 (40303888)
角 大輝  大阪大学, 理学(系)研究科(研究院), 准教授 (40313324)
秋山 茂樹  筑波大学, 数理物質科学研究科(系), 教授 (60212445)
宍倉 光広  京都大学, 理学(系)研究科(研究院), 教授 (70192606)
熊谷 隆  京都大学, 数理解析研究所, 教授 (90234509)
梶野 直孝  神戸大学, 理学(系)研究科(研究院), 准教授 (90700352)
Co-Investigator(Renkei-kenkyūsha) KOTANI Motoko  東北大学, 大学院理学研究科, 教授 (50230024)
KAMEYAMA Atsushi  岐阜大学, 工学部, 教授 (00243189)
OHTA Shin-ichi  京都大学, 大学院理学研究科, 准教授 (00372558)
ITO Shunji  東邦大学, 理学部, 訪問教授 (30055321)
TAKAHASHI Satoshi  奈良女子大学, 人間文化研究科, 准教授 (70226835)
Project Period (FY) 2014-04-01 – 2017-03-31
Keywordsフラクタル / 熱核 / ラプラシアン / Dirichlet form / 力学系 / タイリング
Outline of Final Research Achievements

We have studied the relation between geometric and algebraic structures and analysis on fractals such as self-similar sets and invariant sets of various dynamical systems. For example, we have considered time changes of the Brownian motions on generalized Sierpinski carpets with respect to singular measures. We have established the notion of weakly exponential weakly exponential measures. If a measure is weakly exponential, then we have shown tcertain type of Poincare inequality, the existence of jointly continuous heat kernel and an asymptotic heat kernel estimate using the protodistance associated with the weakly exponential measure.

Free Research Field

解析学基礎・確率論

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Published: 2018-03-22  

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