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Theory of analytic functions and its applications.

Research Project

Project/Area Number 63540117
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

TAKEUTI Akira  Kyoto University Yoshida College Professor, 教養部, 教授 (40026761)

Co-Investigator(Kenkyū-buntansha) KONO Norio  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (90028134)
NISIWADA Kimimasa  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (60093291)
MORIMOTO Yosinori  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (30115646)
UEDA Tetuo  Kyoto University Yoshida College Professor, 教養部, 助教授 (10127053)
ASANO Kiyoshi  Kyoto University Yoshida College Professor Assistant, 教養部, 教授 (90026774)
伊達 悦朗  京都大学, 教養部, 助教授 (00107062)
笠原 皓司  京都大学, 教養部, 教授 (70026748)
Project Period (FY) 1988 – 1989
Project Status Completed (Fiscal Year 1989)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1989: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1988: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsLocal Analytic Transformation / Pseudoconcave Set Of General Order / Singularities of Analytic Sets / Non-linear Cauchy-Kowalevski Theorem / SOS model / Self-similar Function / Estimate of Distribution Tail / 算術幾何平均の正則構造 / 退化シュレディング作用素 / ガウス過程の分布の裾 / 抽象的コーシーコワレフスキ定理
Research Abstract

In our research we pursued the study of the theory of analytic functions and related topics. Below we state the summary of results obtained. I. In the study of the local structure of an analytic transformation of two complex variables,it was a difficult problem to obtain the canonical form of the transformation when one of the eigenvalue of the linear part is equal to I. In this case we succeeded in elucidate the complicated local structure. 2.A property of pseudconvex sets of lower order is found and some new properties of essential singularities if analytic sets are acquainted. 3. A new proof is given to Cox's theorem on the hilomorphic structure of the arithmetic-geometric mean of Gauss. 4. A simplified proof of non-linear Cauchy-Kowalevski theorem,which is fundamental in the theory of PDE,is obtained This proof is based only on the contraction mapping principle. 5.An estimate for degenerate Schrodinger operators is obtained,and applying it some results concerning infinitely degenerate elliptic operators are acquired 6. Star-triangular relations and combinatorial equalities are shown for solid-on-solid(SOS) models in statistical mechanics and their connections with modular functions are clarified. 7.A necessary and sufficient condition for a self-similar function to be absolutely continuous is given. 8. In the study of Gaussian process with non-constant variance,a sharp estimate for the distribution tails is obtained.As for the study of analytic differential systems with singularities,though it was developed considerably,more effort must be continued to integrate the research into publishable form. As stated above,our research established many excellent results in various topics and now still continued,and therefore,further development can be expected.

Report

(3 results)
  • 1989 Annual Research Report   Final Research Report Summary
  • 1988 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] 浅野潔: "A note on the abstract Caushy-Kowalevski theorem" Proc.Japan Acad.64. I02-I08 (1983)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 浅野潔: "A note on the Nash-Moser impricit function theorem" Preprint.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 上田哲生: "local structure of analytic transformations of two complex variables,II." Preprint.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 上田哲生: "Pseudoconcave sets of general order and essential singularities of analytic sets." Preprint.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 森本芳則: "Estimates for degenerate Schroodinger operatoes and hypoellipticity for infinitely degenerate Elliptic operators" Preprint.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 森本芳則: "Propagation of wave front sets and hypoellipticity for degenerate elliptic operators" Pitman res.Notes Math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 伊達悦朗: "Exactly solvable SOS models II.Prrf of the startriangle relation and combinatorial identities" Advanced Studies in Pure Math. 16. 17-122 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 西和田公正: "A holomorphic structure of the arithmetic-geometric mean of Gauss" Proc.Japan Acad.64. 322-324 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 河野敬雄: "The maximum of Gaussian with nonconstant variance:A sharp bound for the distribution tail" Anales of Probability. 17. 632-650 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 河野敬雄: "Functional central limit and loglog law multiplictive systems" Acta Math.Acad.Sci.Hangaricae. 52. 233-238 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 河野敬雄: "On self-affine functions II" Japan J.of Applied Math.5. 441-454 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Asano, Kiyoshi: "A note on the abstract Cauchy-Kowalevski theorem." Proc.Japan Acad.vol.64 102-108, 1988.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Asano, Kiyoshi: "A note on the Mash-Moser imprict function theorem"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Ueda, Tetuo: "Local structure of analytic transformations of two complex Variables, II"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Ueda, Tetuo: "Pseudoconcave sets of general order and essential singularities of analytic sets"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Morimoto, Yoshinori: "Estimates for degenerate Schrodinger operators and hypoellipticity for infinitely degenerate Elliptic operators"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Morimoto, Yoshinori: "Propagation of wave front sets and hypoellipticity for degenerate elliptic operators" Pitman res.Notes Math. vol.183 212-224, 1988.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Date, Eturo: "Exactly solvable SOS models II. Proof of the startriangle relation and combinatorial identities" Advanced Studies in Pure Math vol.16, 17-122, 1988.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Nisiwada, Kimimasa: "A holomorphic structure of the arithmetic-geometric mean of Gauss" Proc.Japan Acad. vol.64 322-324, 1988.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Kono, Norio: "The maximum of Gaussian with nonconstant variance: A sharp bound for the distribution tail" Anales of Probability vol.17 632-650, 1989.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Kono, Norio: "Functional central limit and loglog law for multiplicative systems" Acta Math. Acad.Sci.Hangaricae vol.52, 233-238, 1988.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Kono, Norio: "On self-affine functions II" Japan J.of Applied Math. vol.5.441-454, 1988.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] [1]上田哲生: "Local structure of analytic transformations of two complex variables,II" preprint,pp.35,submitted to Kyoto J.Math.

    • Related Report
      1989 Annual Research Report
  • [Publications] [2]森本芳規: "Estimates for degenerate Schrodinger opeators and hypoellipticity for infinitely degenerate Elliptic operators"

    • Related Report
      1989 Annual Research Report
  • [Publications] [3]伊達悦朗: "Exactly solvsble SOS models II.Proof of the startriangle relation and combinatorial identities" Advanced Studies in Pure Math.,. 16. 17-122 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] [4]西和田公正: "A holomorphic structure of arithmeticgeometric mean of Gauss." Proc.Japan Acad.64. 322-324 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] [5]河野敬雄: "The maximum of Gaussian process with nonconstant variance:A sharp bound bound for the distribution tail" Anales of Probability. 17. 632-650 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 浅野潔: Proc.Japan Acod.

    • Related Report
      1988 Annual Research Report
  • [Publications] 浅野潔: Proc.Japan Acod.

    • Related Report
      1988 Annual Research Report
  • [Publications] 森本芳則: Publ.RIMS.Kyoto Univ.23. (1987)

    • Related Report
      1988 Annual Research Report

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Published: 1988-04-01   Modified: 2016-04-21  

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