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CO-operative Research on Functional Analysis, Real Analisis, and Partial Diffential Equations

Research Project

Project/Area Number 04302007
Research Category

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

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

Principal Investigator

KURODA Shige  Toshi Gakushuin Univ, Fac Sci, Prof, 理学部, 教授 (20011463)

Co-Investigator(Kenkyū-buntansha) KOMATSU Hikosaburo  Univ.of Tokyo, Dept Math Sci, Prof, 数理科学研究科, 教授 (40011473)
MURAMATSU Toshinobu  Univ.of Tsukuba, Math Prof, 数学系, 教授 (60027365)
YAJIMA Kenji  Univ.of Tokyo, Dept Math Sci, Prof, 数理科学研究科, 教授 (80011758)
MURATA Minoru  Tokyo Inst.Tech, Fac Sci, Prof, 理学部, 教授 (50087079)
IGARI Satoru  Tohoku Univ, Fac Sci, Prof, 理学部, 教授 (50004289)
Project Period (FY) 1992 – 1994
Project Status Completed (Fiscal Year 1994)
Budget Amount *help
¥13,700,000 (Direct Cost: ¥13,700,000)
Fiscal Year 1994: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1993: ¥5,500,000 (Direct Cost: ¥5,500,000)
Fiscal Year 1992: ¥5,200,000 (Direct Cost: ¥5,200,000)
KeywordsHarmonic Analysis / Partial Differential Equation / Fourier Analysis / Function Space / Positive Solution / Scattering Theory / 関数解析 / ウエーヴレット / シユレーデインガー方程式 / 擬微分作用素 / スペクトル理論 / 波動作用素 / 退化楕円型作用素
Research Abstract

This research project aimed at investigating problems related to three disciplines mentioned in the title in the spirit of co-operative work and from a unique viewpoint. Results obtained during three years will be itemized below.
1.Methods of Functional and Real Analysis applied to Partial Differential Equations(PDE). Properties of solutions of nonlinear PDE are investigated by these tools and using various results on function spaces. 2.Harmonic Analysis and Complex Analysis. Results are obtained on degenerate elliptic PDE on strongly pseudo-convex domains. These results have some connection with geometry and the theory of probability.
3.Wavelet Analysis. Wavelets theory and related theory of Wilson basis are applied to the prob-lem of asymptotic distribution of eigenvalues of Schrodinger operators and the boundedness of pseudo-differential operators.
4.Asymptotic Analysis, Mathematical Physics.
(1)Application of Asymptotic Analysis to Mathematical Physics of quantum theory.
(2)Various results on scattering theroy are obtaind, notably L^P boundedness of wave operators.
5.Structure of Positive Solutions.Broard investigations are made on the concrete structure of positive solutions of 2nd order parabolic and elliptic PDEs on non relatively compact domains. Here, the investigation is also related to potential theory, geometry, and the theory of probability.
These results manifest clearly strong ties which exist between Rear Analysis, Fourier Analysis, Linear and nonliner PDEs, and Mathematical Physics.Each of these disciplines has certainly its own history of development. We feel that, while pushing researches in each field deeper and deeper, project of co-operative researches from overall viewpoints are much necessary and should be pushed further.

Report

(4 results)
  • 1994 Annual Research Report   Final Research Report Summary
  • 1993 Annual Research Report
  • 1992 Annual Research Report
  • Research Products

    (46 results)

All Other

All Publications (46 results)

  • [Publications] Kuroda,Shige Toshi: "Topics in the spectral methods in numerical computation-Product formulas,Differential Equations with Applications to Mathematical Physics" W.F.Ames et al eds.,Academic Press. 213-219 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Igari,Satoru: "Operating functions on Fourier multipliers" Tohoku Math.J.40. 357-366 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Murata,Minoru: "Sufficient condition for non-uniqueness of the positive Cauchy problem for parabolic equations,Spectral and Scattering Theory" Advanced Studies in Pure Math.23. 275-282 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Yajima,Kenji: "The W^<k.P>-continuity of wave operators for Schrodinger operators" Proc.Japan Acad.69(A). 94-98 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Muramatsu,Toshinobu: "Abstract Besov spaces approach to the non-stationary Navier-Stokes equations" Mathematical Methods in the Applied Mathematics. 15. 599-620 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Komatsu,Hikosaburo: "Hyperfunctions,ultradistributions and microfunctions,Generalized Functions and their Applications" Plenum,New York. 119-220 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Fujiwara,Daisuke: "Stationary Phase method with an estimate of the remainder term over a space of large dimension.Spectral and scattering theory" Marcel Decker,New York. 161. 1-14 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Ikebe,Teruo: "The Schrodinger operator with a pentrable wall interaction" J.d´Anal.Math.59. 37-43 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Masuda,Kyuya: "Asymptotic behaviour of solutions of reaction-diffusion systems of Litka-Volterra type" J.Differential and Integral Equations. 7. 1043-1053 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Miyachi,Akihiko: "Extension theorems for the function spales of Devore and Sharpley" Math.Japonica. 38. 1033-1049 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Tamura,Hideo: "Scattering theory for N-particle systems with Stark effect;asymptotic completeness" Publ.RIMS Kyoto Univ.29. 69-884 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Kuroda,Shige Toshi: "量子物理の数理" 岩波書店, 129 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Itoh,Seizo: "Diffusion Equations," Amer.Math.Soc., 225 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Kuroda, Shige Toshi: "Topics in the spectral methods in numerical computation-Product formulas, DDifferential Equations with Applications to Mathematical Physics" W.F.Ames et al eds., Academic Press. 213-219 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Igari, Satoru: "Operating functions of Fourier multipiers" Tohoku Math.J. 40. 357-366 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Murata, Minoru: "Sufficient condition for non-uniqueness of the positive Cauchy problem for parabolic equations, Spectral and Scattering Theory." Advanced Studies in Pure Math.23. 275-282 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Yajima, Kenji: "The w^<K,P> -continuity of wave operators for Schrodinger operators" Proc.Japan Acad. 69. 94-98 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Muramatsu, Toshinobu: "Abstract Besov spaces approach to the non-stationary Navier-Stokes equations" Mathematical Methods in the Applied Mathematics. 15. 599-620 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Komatsu, Hikosaburo: "Hyperfunctions, ultradistribu-tions and microfunctions, Generalized Functions and their Applications" Plenum, New York. 119-220 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Fujiwara, Daisuke: "Stationary phase method with an estimate of the remainder term over a space of large dimension. Spectral and scattering theory" Marcel Decker, New York. 161. 1-14 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Ikebe, Teruo: "The Schrodinger operator with a penetrable wall interaction" J.d'Anal.Math.59. 37-43 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Masuda, Kyuya: "Asynptotic behavior of solutions of reaction-diffusion systems of Litka-Volterra type" J.Differential and Integral Equations. 7. 1041-1053 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Miyachi, Akihiko: "Extension theorems for the function spaces of DeVore and Sharpley" Math.Japonica. 38. 1033-1049 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Tamura, Hideo: "Scattering theory for N-particle systems with Stark effect ; asymptotic completeness" Publ.RIMS Kyoto Univ.29. 69-884 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Kuroda, Shige Toshi: An Introduction to Mathematics of Quantum Physics. Iwanami, 129 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] ITOH,Seizo: Diffusion Equations. Amer.Math.Soc, 225 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Arai,Hitoshi: "Degenerate elliptic operators,Hardy spaces and diffusions on strongly pseudoconvex domains" Tohoku Math.J.,to appear.

    • Related Report
      1994 Annual Research Report
  • [Publications] Fujiwara,Daisuke: "Stationary phase method with an estimate of the remainder term overa space of large mimension" Lecture Notes in Pure and Applied Mathematics. 161. 1-14 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Murata,Minoru: "Sufficient condition for non-uniqueness of the positive Cauchy problem for parabolic equations" Kinokuniya. 275-282 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Nakamura,Shu: "Low energy asymptotics for Schrodinger operators with slowly decreasing potentials" Commun.Math.Phys.161. 63-76 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Tachizawa,Kazuya: "The boundedness of pseudodifferential operators on modulation spaces" Math.Nachrichten. 168. 263-277 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Kuroda,Shigetoshi: "量子物理の数理" 岩波書店, 129 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Yajima,Kenji: "数理物理学入門" 東京大学出版会, 334 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Igeri,S.(Sato,E.): "Operating functions on Fourier multipliers" Tohoku Math.Journ.(発表予定).

    • Related Report
      1993 Annual Research Report
  • [Publications] Fujiwara,D.: "Some Feynmann path integrals as oscillatory integrals over a Sobolev manifold" Lecture Notes in Math.,Springer (Functional Analysis and Related Topics). No.1540. 39-53 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Murata,M.: "Uniform restricted parabolic Harnack inequality,separation principle,and ultra contractivity for parabolic equations" Lecture Notes in Math.,Springer (Functional Analysis and Related Topics). No.1540. 277-288 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Tamura,H.: "Scattering theory for N-particle systems with stark effect:asymptotic completeness" Publ.RIMS Kyoto Univ.29. 869-884 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yajima,K.: "The W k,p-continuity of wave operators for Schrodinger operators" Proc.Japan Acad.,Ser.A. 69. 94-98 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Tachizawa,K.: "The boundedness of pseudodifferential operators on modulation spaces" Math.Nachr.(発表予定).

    • Related Report
      1993 Annual Research Report
  • [Publications] Uajima,Kenji: "Gevrey frequency set and semi-classical behaviour of wave packets" Schrodinger Operators,the Quantum Mechanical Many-Body Problem,Lect.Notes in Phys.403. 248-264 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Kuroda,S.T.: "Topics in the spectral methods in numerical computation" Differntial Equations with Applications to Mathematical Physics,Academic Press. 213-219 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Tamura,Hideo: "Semi-classical asymptotics for total scattering cross sections of 3-body systems" J.Math.Kyoto Univ.32. 533-555 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Arai,Hitoshi: "Area integrals for Riesz measures on the Siegel upper half space of type II" Tohoku Math.J.44. 613-662 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Miyachi,Akihiko: "Extension theorem for the function spaces of DeVore and Sharpley" Mathematica Japonica,to appear.

    • Related Report
      1992 Annual Research Report
  • [Publications] Muramatsu,Toshinobu: "Abstract Besov spaces approach to the non-stationary Navier-Stokes equations" Math.Meth.in Appl.Math.15. 599-620 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Ito,Seizo: "Diffusion Equations" American Mathematical Society, 225 (1992)

    • Related Report
      1992 Annual Research Report

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Published: 1992-04-01   Modified: 2016-04-21  

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