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1996 Fiscal Year Final Research Report Summary

Analysis of a Gaussian measure

Research Project

Project/Area Number 08454044
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKYUSHU UNIVERSITY

Principal Investigator

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

Co-Investigator(Kenkyū-buntansha) 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 Period (FY) 1996
KeywordsSierpinski gasket / Martin boundary / random translation / fractal / density theorem / almost complex structure / similar translations / multiplicative chaos
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 two-valued 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 sigma-finite 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.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] R.Fukuda: "Ф-density theorem on a metric space." Kyushu Journal of Mathematics. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Mizumachi: "Absolute continuity of similar translations." J.Math.,Kyoto University. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kunita: "Stochastic flows with selfsimilar properties" Stochastic analysis and applications. (Ed.by Davies,Truman and Elwortry). 286-300 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Shiohama: "Cut loci and distance spheres on Alexandrov surfaces" Seminairs et Congres,Collection SMF 1. 531-560 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Taniguchi: "On almost complex structures on abstract Wiener spaces." Osaka J.Math.33. 189-206 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Sugita: "Holomorphic Wiener function" proceedings of Taniguchi Symposium '94 at Warwick University. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] R.Fukuda: "PHI-density theorem on a metric space." Kyushu J.Math.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Mizumachi: "Absolute continuity of similar translations." J.Math., Kyoto Univ.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kunita: "Stochastic flows with selfsimilar properties" Stochastic analysis and applications. (Ed.by Davies, Truman and Elworthy) World Scientific. 286-300 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Shiohama: "Cut loci and distance spheres on Alexandrov surfaces" Seminairs et congres, Collection. SMF 1. 531-560 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Taniguchi: "On almost complex structures on abstract Wiener spaces." Osaka J.Math.33. 189-206 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Sugita: "Holomorphic Wiener function." Proc.of Taniguchi Symposium '94 at Warwick University.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1999-03-09  

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