• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

1993 Fiscal Year Final Research Report Summary

Special Function of Several Variables

Research Project

Project/Area Number 04302005
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionKobe University

Principal Investigator

TAKANO Kyoichi  Kobe Univ., Dep. of Math., Prof., 理学部, 教授 (10011678)

Co-Investigator(Kenkyū-buntansha) YOSHIDA Masaaki  Kyushu Univ., Dep. of Math., Prof., 理学部, 教授 (30030787)
MAJIMA Hideyuki  Ochanomizu Univ., Dep. of Math., Prof., 理学部, 教授 (50111456)
KOHNO Mitsuhiko  Kumamoto Univ., Dep. of Math., Prof., 理学部, 教授 (30027370)
KIMURA Hironobu  Univ. of Tokyo, Dep. of Math., Asso. Prof., 大学院・数理科学研究科, 助教授 (40161575)
OKAMOTO Kazuo  Univ. of Tokyo, Dep. of Math., Prof., 大学院・数理科学研究科, 教授 (40011720)
Project Period (FY) 1992 – 1993
Keywordshypergeometric function / confluent HG function / twisted homology / twisted cohomology / confluce process / monodromy group / Stokes phenomenon / connection coefficient
Research Abstract

1. On the study of (k, n) type hypergeometric functions (We abbreviate hypergeomentric as HF) : (1) The theory of twisted homologies and twisted cohomologies and interesection numbers was developed. We proposed a general framework based on the algebraic topology of the configulation spaces of n-points. A twisted simplicial theory and a twisted singular theory for the configulation spaces was developped and the exterior power structure of the homology module associated with the HG system of (3,6) type was obtained and all the cases where the group is of frute order were determined. (3) The relation between contiguous operators operators and the b functions for HG functions were obtained.
2. On the study of(k, n)lambda type HG functions where lambda=(lambda_1, ・・・ lambda_1) is the decomposition of n : (1) The structure of the Lie algebra generated by contiguous operators for (k, n)lambda type HG functions was determined. (2) We found a limit process which reduces (k, n)lambda type HG functions (or system) to (k, n)mu type HG functions (or system) where mu is adjacent to lamdba. The process is just the confluence from Gauss to Kummer in the case where k = 2, n = 4 and lambda = (1,1,1,1), mu = (2,1,1,1). It acts well on Jodan groups, on characters and on differential equations.
3. On asymptotic analysis : A general methpd of asymptotic for confluent HG functions was proposed. It consists of three parts : the first is Borel Transformation, the second is an analysis of the resurgent equation and the last is Laplace transformation. Based on the method, Stokes multipliers for the confluent HG two variables were calculated.

  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] 木村弘信: "On confluences of the general hypergeometric systems" Proc.of the Japan Academy. 69. 99-104 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 原岡喜重: "Contiguity relations of generalized confluent hypergeometric functions" Proc.of the Japan Academy. 69. 105-110 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 下村俊: "Asymptotic expansions and Stokes multipliers of the confluent hypergeometric function Ф_2,I" Proc.Roy.Soc.Edinburgh. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 岩崎克則: "Twisted homology of the configulation spaces of n-points with application to the hypergeometric functions" Preprint Series:University of Tokyo,Department of Mathematical Sciences. 94-11. 1-68 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 喜多通武: "On hypergeometric functions in several variables II,The Wronskian of the hypergeometric functions" J.Math.Soc.Japan. 45. 645-669 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 松本圭司: "Monodromy of the hypergeometric differential equation of type(3,6)I" Duke Math.J.71. 403-426 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 高野恭一: "常微分方程式" 朝倉書店, 210 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Aizawa, K.and Tmita, Y.: "Unbounded viscosity solutions of fully nonlinear elliptic equations in R^n" Adv. Math. Sci. Appl.2. 297-316 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Gerard, R.and Tahara, H.: "Solutions holomorphes et singulieres d'equations aux derivees partielles sigulieres nonlineaires" Publ. RIMS, Kyoto Univ.29. 121-151 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Haraoka, Y.and Kimura, H.: "Contiguity relations of generalized confluent hypergeometric functions" Proc. Japan Acad. 69. 105-110 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Iwasaki, K.: "On a dynamical system on the matrix algebra, preprint series" Univ. of Tokyo. 94-3. 1-45 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Iwasaki, K.and Kita, M.: "Exterior power structure of the twisted de Rham cohomology associated to arrangements of hyperplanes in general position, preprint series" Univ. of Tokyo. 94-2. 1-26 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Iwasaki, K.and Kita, M.: "Twisted homology of the configulation spaces of n-points with application to the hypergeometric functions" preprint series, Univ. of Tokyo. 94-11. 1-68 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kamimura, Y.: "An inverse problem in bifurcation theory" J.Differential Equations. 106. 10-26 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kamimura, Y.: "An inverse problem in bifurcation theory II" J.Math. Soc. Japan.46. 89-110 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kawai, T.and Takei, Y.: "On the structure of Painleve transcendents with a large parameter" Proc. Japan Acad.69. 224-229 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kimura, H., Haraoka, Y.and Takano, K.: "The generalized confluent hypergeometric functions" Proc. Japan Acad.68. 290-295 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kimura, H., Haraoka, Y.and Takano, K.: "On confluence of the general hypergeometric systems" Proc. Japan Acad.69. 99-10 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kita, M.: "On hypergeometric functions in several variables I.New integral representaions of Euler type" Japan. J.Math. 18. 25-74 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] KIta, M.: "On hypergeometric functions in several variables II.The Wronskian of the hypergeometric functions." J.Math. Soc. Japan. 45. 645-669 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Majima, H.: "Stokes structures of the confluent hypergeometric differential equations in two variables and resurgent equations, preprint" (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Matsumoto, K., Sasaki, T., Takayama, N.and Yoshida, M.: "Monodromy of the hypergeometric differential equation of type (3, 6) (I)" Duke Math. J.71. 403-426 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Matsumoto, K., Sasaki, T., Takayama, N.and Yoshida, M.: "Monodromy of the hypergeometric differential equation of type (3, 6) (II)20GD16 : to appear in Ann. Scuola Norm Sup. Pisa"

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Matsumoto, K.and Yoshida, M.: "Configulation space of 8 points on the projective line and a 5-dimensional Picard modular group" Compositio Math.86. 265-280 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Miyake, M.: "Relations of equations of Euler, Hermite and Weber via the heat equation" Funkcial. Ekvak.36. 251-273 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Shimomura, S.: "Asymptotic expansions and Stokes multiplies of the confluent hypergeometric function PHI_2, I." Proc. Roy. Soc. Edinburgh.123. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Terasoma, T.and Saito, T.: "A determinant formula for period integrals" Proc. Japan Acad.69. 131-135 (1993)

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

URL: 

Published: 1995-03-27  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi