Project/Area Number  08454044 
Research Category 
GrantinAid for Scientific Research (B)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  KYUSHU UNIVERSITY 
Principal Investigator 
SATO Hiroshi Graduate School of Mathematics, KYUSHU UNIVERSITY,Professor, 大学院・数理学研究科, 教授 (30037254)

CoInvestigator(Kenkyūbuntansha) 
HAMANA Yuji Graduate School of Mathematics, KYUSHU UNIVERSITY,Assistant Professor, 大学院・数理学研究科, 講師 (00243923)
SUGITA Hiroshi Graduate School of Mathematics, KYUSHU UNIVERSITY,Associate Professor, 大学院・数理学研究科, 助教授 (50192125)
TANIGUCHI Setsuo Graduate School of Mathematics, KYUSHU UNIVERSITY,Associate Professor, 大学院・数理学研究科, 助教授 (70155208)
SHIOHAMA Katsuhiro Graduate School of Mathematics, KYUSHU UNIVERSITY,Professor, 大学院・数理学研究科, 教授 (20016059)
KUNITA Hiroshi Graduate School of Mathematics, KYUSHU UNIVERSITY,Professor, 大学院・数理学研究科, 教授 (30022552)

Project Fiscal Year 
1996 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥3,500,000 (Direct Cost : ¥3,500,000)
Fiscal Year 1996 : ¥3,500,000 (Direct Cost : ¥3,500,000)

Keywords  Sierpinski gasket / Martin boundary / random translation / fractal / density theorem / almost complex structure / similar translations / multiplicative chaos / 絶対連続性 / フラクタル / 密度定理 / 概複素構造 / random franslation 
Research Abstract 
We have finished this research project almost successfully. The absolute continuity of the similar random translations of an IID random sequence we have investigated in detail and almost elucidated. (see reference 2) On the absolute continuity of the twovalued random translations of an IID random sequence we have refined and simplifyed the necessary and sufficient conditions of Sato and Tamashiro (1994) from a new point of view, and given a clear negative answer to a conjecture of J.P.Kahane on the multiplicative chaos. (in preparation) We have exposed these results in the International Symposium on Analysis and Probability at Taipei. They will provide an illuminating example in the investigation of the absolute continuity of random translations. Let lambda be a sigmafinite measure on a metric space with the local density theorem and psi be a nonincreasing function on the positive half line. If lambda is the Lebesgue measure Calderon & Zygmund (1953) proved that a class of psi satisfies the global density theorem. We have extended this theorem to the general metric space. (reference 1) We have succeeded in representing the Sierpinski gasket as a Martin boundary of a Markov chain on the tree. (in preparation) This is a nice result and provids a new approach to the investigation of fractals. This research is a joint work with M.Denker (Gottingen). We have also invited R.D.Mauldin (North Texas) and discussed on those subjects. Taniguchi, and Sugita established the almost complex structures and some complex analysis of abstract Wiener spaces.
