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関数解析的手法による位相力学系の研究

Research Project

Project/Area Number 09640149
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KAWAMURA Shinzo  Mathermatical Sciences, Yamagata Univ. Professor, 理学部, 教授 (50007176)

Co-Investigator(Kenkyū-buntansha) OKAYASU Takateru  Mathematical Sciences, Yamagata Univ. Professor, 理学部, 教授 (60005775)
UCHIDA Fuichi  Mathematical Sciences, Yamagata Univ. Professor, 理学部, 教授 (90028126)
TOMIYAMA Jun  Mathematics, Japan Women's Univ. Professor, 理学部, 教授 (30006928)
SATO Enji  Mathematical Sciences, Yamagata Univ. Professor, 理学部, 教授 (80107177)
MORI Seiki  Mathematical Sciences, Yamagata Univ. Professor, 理学部, 教授 (80004456)
水原 昂廣  山形大学, 理学部, 教授 (80006577)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1997: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywordstopological dynamics / chaotic dynamics / wavelets theory / operator algebras / transformation group / operator theory / meromorphic maps / multiplier / ウェブレット理論 / 作用素論 / コンパクトアーベル群 / ウェヴレット理論 / モリー空間 / 超越的有理写像 / モリ-空間
Research Abstract

(1) S. Kawamura who is the head investigator organized two workshops in UNCC and Yamagata University in the beginning and the end of 1999 respectively. Moreover he studied chaotic maps on metric measure space. As a way of studying he used the theory of operator algebras and obtained some important results concerning chaos maps and wavelets theory.
(2) J. Tomiyama has clarified the structure of bounded orbit equivalence of topological dynamical systems for the interplay between topolocicl dynamics and C*-theory. He also classified the ideals of homeomorphism C*-algebras to show their structure in connection with the general isomorphism problem.
(3) F. Uchida showed behavior of smooth actions of non-compact semi-simple Lie groups. Moreover he clarified construction and classification concerning smooth actions of Sp(p,q) on the (4p+4q-1)-sphere.
(4) T. Okayasu obtained some important results concerning Lowener-Hainz inequalties in Banach*-algebras and a multivariable von Neumann's inequality.
(5) S. Mori proved, for any given transcendental meromorphic mapping of CィイD1mィエD1 into PィイD1nィエD1(C), that one can eliminate all defects (deficient hyperplanes, deficient hypersurfaces) and defects of rational moving targets by a small deformation of the mapping, and also proved that meromorphic mappings without defects in dense in a space of transcendental meromorphic mappings.
(6) E. Sato studied the Banach algebra M(p,q), which is defined by the translation invariant operators from Lp(G) to Lq(G) on infinite compact abelian groups. Also I studied the transference of continuity from maximal Fourier multiplier operators on n-dimensional Euclidian space to those on n-dimensional torus.

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report

Research Products

(37 results)

All Other

All Publications (37 results)

  • [Publications] S.Kawamura: "Covariant representations associated with chaotic dynamical system"Tokyo Jour. Math.. 20. 205-217 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J.Tomiyama: "Representation of topological dynamical system and C^*-algebras"Contemporary Math.. 228. 351-364 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] F.Uchida: "On smooth SO_0(p,q)-actions on S^<p+q-1>"Tohoku Math. Jour.. 49. 185-202 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T.Okayasu: "The Lowner-Heinz inequality in Banach^*-algebras"Glasgow Math. Jour.. 42. 243-246 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Mori: "Elimination of defects of meromorphic mapping of Cm into Pn(C)"Annales Acad. Sci. Fenn Math.. 24. 89-104 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Kaneko and E.Sato: "Notes on transference of continuity from maximal Fourier multiplier operators on R^n to those on T^n"Interdisplinary Information Sciences. 4. 97-107 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Kawamura: "Covariant representations associated with chaotic dynamical systems."Tokyo Jour. Math.. 20 No.1. 205-217 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Boyle and J. Tomiyama: "Bounded topological orbit equivalence and C*-algebras"Jour. Math. Soc. Japan. 50. 317-329 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J. Tomiyama: "Representation of topological dynamical systems and C*-algebras"Contemporary Math.. 228. 351-364 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J. Tomiyama: "Structure of ideals and isomorphism problems of C*-crossed products by single homeomorphisms"Tokyo Jour. Math.. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] F. Uchida: "On smooth SOィイD2oィエD2(p,q)-actions on SィイD1pィエD1 + q - 1, II"Tohoku Math. J.. 49-2. 185-202 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Okayasu: "The Lowner-Heinz inequality in Banach*-algebras."Glasgow Math. Journ.. 42. 243-246 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Okayasu: "A multivariable von Neumann's inequality"The Proc. Of the Second International ISAAC 99 Congress.. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Mori: "Elimination of defects of meromorphic mappings of CィイD2mィエD2 into PィイD2nィエD2(C)"Annales Academic Scientiarum Fennicae Mathematica. 24. 89-104 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Mori: "Elimination of defects of meromorphic mappings by small deformation"Recent Developments of Complex Analysis and computer Algebra, Kluwer Academic Publishers. 247-258 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Mori: "Defects of holomorphic curves into PィイD1nィエD1(C) for rational moving targets"Research Reports of the Nevanlinna Theory and its Applications II, Nippon Institute of Technology. 1999. 60-65

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Arai and T. Mizuhara: "Morrey spaces on spaces of homogeneous type and estimates for □ィイD2bィエD2 and the Cauchy-Szego projection"Math. Nachr.. 185. 5-20 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Abe and E. Sato: "On the Banach algebra M (p,q) (1≦p<q≦∞"Tokyo Jour. Math.. 20. 219-242 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Kaneko and E. Sato: "Notes on transference of continuity from maximal Fourier multiplier operators on RィイD1nィエD1 to those on TィイD1nィエD1"Interdisciplinary Information Sciences. 4. 97-107 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Kawamura: "Chaotic maps on metric measure spaces and behavior of states"京大数理解析研究所講究録に発表予定. (未定).

    • Related Report
      1999 Annual Research Report
  • [Publications] J.Tomiyama: "Structure of ideals and isomorphism problems of C^<n*>-crossed products by single homeomorphism."Tokyo Jour. Math に発表予定. (未定).

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Okayasu: "The Lowner-Heinz inequality in Banach^*-algebras"Glasgow Math, Jour.. 42. 243-246 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Okayasu: "Amultivariable von Neumaun's inequality"Proc, ISAAC 99 Congress に発表予定. (未定).

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Mori: "Elimination of defects of meromorphie mapping of Cn into Pn(C)"Annales Acad. Sci. Fenn, Math. 24. 89-104 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Mori: "Defects of holomorphic curves into P^n(C) for rational moving targets"Research Rep. Nevanlinna Theory and its Appl. II. 60-65 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] M.Boyle and J.Tomiyama: "Bounded topological orbit equivalence and C^*-algebras" Jour.Math.Soc.Japan. 50. 317-329 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] J.Tomiyama: "Structure of ideals and isomorphisms of C^*-crossed product by single homeomorphism." Tokyo Jour.Math.掲載予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Okayasu: "The Lowner-Heinz inequality in Banach^*-algebras" Glasgow Math.Jour.掲載予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Kaneko and E.Sato: "Notes on transference of continuity from maximal Fourier multiplier operators on R^n to those on T^n" Interdisplinary Information Sciences. 4. 97-107 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Mizuhara: "Recent topics on commutators and Morry spaces" 調和解析セミナー報告集. 23-36 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Mizuhara: "Commutators of single integral operators on Morry spaces with general growth functions" 京都大学数理解析研究所講究録. 掲載予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Kawamura: "Covariant representations associated with chaotic dynamical systems" Tokyo J.Math.20・1. 205-207 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] F.Uchida: "On smooth SUo(P、q)-actions on S^<P+q-1>,II" Tohoku Math.J.49・2. 185-202 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Mori: "Elimination of defects of meromorphic mapping of C^m into P^n (C)" Ann.Acad.Sci.Fenn. 23(発表予定). (998)

    • Related Report
      1997 Annual Research Report
  • [Publications] E.Sato: "On the Banach algebra M (P.q) (1≦P<q≦∞)" Tokyo J.Math. 20・1. 219-242 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Kaneko, E.Sato: "Notes on transference of continuity from maximal Fourier multiplier operators on R^n to those on T^n" Interdisciplinary Information Science. 1・1(発表予定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Arai, T.Mizuhara: "Morry spaces on spaces of homogeneous type and estimates for □b and the Cauchy-Szego projection" Math.Nachr.185. 5-20 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-03-31   Modified: 2016-04-21  

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