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Research in Functional Analsys and Mathematical theory of Feynman path integrals.

Research Project

Project/Area Number 11640180
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionGakushuin University

Principal Investigator

FUJIWARA Daisuke  Gakushuin Univ.Dept.of Math.Prof., 理学部, 教授 (10011561)

Co-Investigator(Kenkyū-buntansha) MIZUTANI Akira  Gakushuin Univ.Dept.of Math.Prof., 理学部, 教授 (80011716)
KATASE Kiyoshi  Gakushuin Univ.Dept.of Math.Prof., 理学部, 教授 (70080489)
KURODA Shigetoshi  Gakushuin Univ.Dept.of Math.Prof., 理学部, 教授 (20011463)
SUGANO Satoko  Gakushuin Univ.Dept.of Math.Assist., 理学部, 教授 (50316931)
WATANABE Kazuo  Gakushuin Univ.Dept.of Math.Assist., 理学部, 助手 (90260851)
川崎 徹郎  学習院大学, 理学部, 助教授 (90107061)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2000: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
KeywordsFeynman path integrals / Oscillatory integrals / Schrodinger equation / Stationary phase / Selfajoint operator / Quantum mechanics / WKB-method / path integrals / シュレーディングー方程式 / 位相停留法 / 汎関数解析 / Foureir積分作用素 / 準古典近似 / Schrodinger方程式
Research Abstract

1. Fujiwara tried to give mathematically rigorous treatment of Feynman path integrals. It may seem possible to get a new proof of Kumanogo-Taniguchi theorem for actions with electro-magnetic fields if we cleverly conbine N.Kumanogo's method to that of our work which were published in 1997. Fujiwara wrote a textbook published by Springer Verlarg Tokyo in 1999. The english translation of the title is "Mathematical Method of Feynman path integrals".
2. S.T.Kuroda together with P.Kurasov of Stockholm University showed that the Krein's formula describing relations of self-adjoint extension of two operators can be understood as resolvent equation between two operators. And they dicussed H_∈-perturbation theory.
3. Mizutani studied finite element methods for parabolic nonlinear partial differential equations.
4. Watanabe togeher with Kurasov of Stockholm Univ. studied H_4 realization of selfadjoint extension of operators.
5. Sugano together with Kurata of Metropolitan Univ. studied fundamental solutions of uniformly elliptic operators with potentials in a class of functions which is a generalization of the class of positive polynomials. They suceeded in proving their fundamental solutions show good behviour in the weighted L^p space and Morrey classes. Using these facts, they proved a good estimates of distribution of eigen values and sharp information for order of decay of eigen functions of their elliptic operators.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] S.T.Kuroda and P.Nagatani: "H_∈-construction and some applications"Operator Theory. 108. 99-105 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.T.Kuroda and P.Kurasov: "Krein's formula and perturbation theory"Research report in Math.Depart.Stockholm Univ.. 6. (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Watanabe and P.Kurasov: "On H_△-perturbation of self-adjoint operators."Research report in Math.Depart.Stockholm Univ.. 16. 1-18 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Sugano and K.Kurata: "A remark of estimates for uniformly elliptic operators on weighted L^p spaces and Morrey spaces."Maht.Nachrich.. 209. 137-150 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Sugano and K.Kurata: "Fundamental solution, eigenvalueasymptotics and eigenfunctions of degenerate elliptic operators with positive potentials,"Studia Math.. 138. 101-119 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Sugano,K.Kurata and S.Nishigaki: "Boundedness of integral operators on generalized Morrey spaces and its application to Schrodinger operators,"Proc.Amer.Math.Soc.. 128. 1125-1134 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 藤原大輔: "ファインマン経路積分の数学的方法-時間分割近似法-"シュプリンガーフェアラーク・東京. 275 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.T.Kuroda (with N.nagatani): "H_∈-construction and some applications"Operator Theory. 108. 99-105 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.T.Kuroda (with P.Kurasov): "Krein's formula and perturbation theory"Research report in Math.Depart.Stockholm Univ.. 6. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Watanabe (with P.Kurasov): "On H_Δ-perturbation of self-adjoint operators"Research report in Math.Depart. Stockholm Univ.. 16. 1-18 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Sugano (with K.Kurata): "A remark of estimates for uniformly elliptic operators on weighted L^p spaces and Morrey spaces"Math.Nachrich. 209. 137-150 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Sugano (with K.Kurata): "Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic opeartors with positive potentials"Studia Math. 138. 101-119 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Sugano (with K.Kurata and S.Nishigaki): "Boundedness of integral operators on generalized Morrey spaces and its application to Schrodinger operations"Proc.Amer.Math.Soc.. 128. 1125-1134 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Sugano (with K.Kurata): "Estimates of the fundamental solution for magnetic Schrodinger operators and their applications"Tohoku Math.J.. 52. 367-382 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] D.Fujiwara: "Mathematical methods for Feynman path integrals-time slicing approximataion-"Springer Verlag, Tokyo (In Japanese). 1-275 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.T.Kuroda and P.Nagatani: "Н_ε-construction and some applications"Operator Theory. 108. 99-105 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.T.Kuroda and P.Kurasov: "Krein's formula and perturbation theory"Research report in Math.Depart.Stockholm Univ.. 6. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Watanabe and P.Kurasov: "On Н_△-perturbation of self-adjoint operators."Research report in Math.Depart.Stockholm Univ.. 16. 1-18 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Sugano and K.Kurata: "A remark of estimates for uniformly elliptic operators on weighted L^p spaces and Morrey spaces."Maht.Nachrich.. 209. 137-150 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Sugano and K.Kurata: "Fundamental solution, eigenvalueasymptotics and eigenfunctions of degenerate elliptic operators with positive potentials,"Studia Math.. 138. 101-119 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Sugano,K.Kurata and S.Nishigaki: "Boundedness of integral operators on generalized Morrey spaces and its application to Schrodinger operators,"Proc.Amer.Math.Soc.. 128. 1125-1134 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 藤原大輔: "ファインマン経路積分の数学的方法-時間分割近似法-"シュプリンガーフェアラーク・東京. 275 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Naondo Jin: "Un maximality of two-sheeted unlimited covering surfaces of the unit disc"J.of Math.of Kyoto Univ.. vol.39. 155-183 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Satoko Sugano(with Kazuhiro Kurata): "A remark on estimates for uniformly elliptic operators on weighted $L^p$ spaces and Morrey spaces"Math.Nachr. 209. 137-150 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 藤原大輔: "ファインマン経路積分の数学的方法"シュプリンガー・フェアラーク東京. 277 (1999)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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