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1996 Fiscal Year Final Research Report Summary

Number theoretic and algebraic research of divergent formal solution

Research Project

Project/Area Number 07640250
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionCHUO UNIVERSITY

Principal Investigator

YOSHINO Masafumi  CHUO UNI., ECONOMICS,Professo, 経済学部, 教授 (00145658)

Project Period (FY) 1995 – 1996
KeywordsToeplitz / formal solutions / hypoellipticity / WKB method / Newton polygone / vector fields / normal form
Research Abstract

In this research we introduced a new method based on Toeplitz operator theory, WKB analysis and generalized implicit function theorem in dealing with divergent formal power series solutions. Our method can be applied to global and local hypoelipticity of operators, index formula of a system of (partial and ordinary) differential operators on various function spaces and (local)normal forms of commuting systems of singular vector fields and diffeomorphisms. These results revealed transcendental phenomena in the theory of differential operators and the role or rapidly convergent iteration method with infinite loss of derivatives. This research will continue as a collaborations with Italian and English researchers. We will give short items of our results.
1. Index formula of systems of irregular singular ordinary differential operators in formal Gevrey spaces via Toeplitz symbols.
2. Necessary and sufficient conditions for irregular singular type partial differential operators with two independent variables.
3. To determine critial Gevrey indices for solvability and regularity of degenerate parabolic operators via Newton polygones.
4. Necessary and sufficient conditions for the reduction to their normal forms of commuting systems of resonant singular vector fields.
5. WKB analysis to global solvability and regularity of mixed type operators on the torus.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] 吉野正史,三宅正武: "Toeplitz operators and an index theorem for differential operators …" Funkcial.Ekvac.38(2). 329-342 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉野正史,T.Gramchev: "WKB analysis to global solvability and hypoellipticity" Publications of RIMS,Kyoto Univ.31. 443-464 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉野正史,三宅正武: "Fredholm property of partial diff.operators of irregular …" Arkiv for Mat.33. 323-341 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉野正史,P.Popivanov他: "Critical Gevrey index for Gevrey hypoellipticity …" Annali di Mat.Puraed applicata. CLXX. 103-131 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉野正史,三宅正武: "Necessary conditions for Fredholmness of partial …" Publications of RIMS. (出版予定). (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉野正史,T.Gramchev: "First order pseudodifferential operators on the torus" Ann.Univ.Ferrara. (出版予定). (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Masafumi YOSHINO and M.Miyake: "Toeplitz operators and an index theorem for differential operators on Gevrey spaces" Funkcial.Ekvac. 38 (2). 329-243 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masafumi Yoshino and T.Gramchev: "WKB analysis to global solvability and hypoellipticity" Publications of RIMS,Kyoto Univ. 31. 443-464 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masafumi YOSHINO and M.Miyake: "Fredholm property of partial differential operators of irregular singular type" Arkiv for Mat. 33. 323-341 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masafumi YOSHINO,T.Gramchev andP: "Polivanov, Critical Gevrey index for Gevrey hypoellipticity or parabolic operators" Annali di Matematica pura ed applicata, (IV). Vol. CLXX. 103-131 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masafumi YOSHINO and M.Miyake: "Necessary conditions for Fredholmness of partial differential operators of irregular singular type" Publications of RIMS,Kyoto University. (to be published).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masafumi YOSHINO,D.Dicknson andT: "Gramchev, First order pseudodfiiferential operators on the torus : normal forms, Diophantine phenomena and global hypoellipticity" Ann.Univ.Ferrara. (to be published).

    • 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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