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2003 Fiscal Year Final Research Report Summary

THE RESARCH OF PERATORS ON FUNCTION SPACES BY THE METHOD TO HARMONIC ANALYSIS AND RELATED ANALYSIS

Research Project

Project/Area Number 14540150
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionYAMAGATA UNIVERSITY

Principal Investigator

SATO Eiji  YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (80107177)

Co-Investigator(Kenkyū-buntansha) MIZUHARA Takahiro  YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (80006577)
MORI Seiki  YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (80004456)
OKAYASU Takateru  YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (60005775)
KAWAMURA Shinzo  YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (50007176)
仲田 正躬  山形大学, 理学部, 教授 (20007173)
Project Period (FY) 2002 – 2003
KeywordsLorentz space / Hankel transform / k-hyponormal operators / deficiency / commutator / Juia set / probability densety function / Mobious transformation
Research Abstract

Our purpose of this research is to study the properties of operators on function spaces by the method of harmonic analysis and related analysis. Our investigators did the research at each special point. The content is as follows:
Sato studied the generalization of the relation between some operators of Hankel transforms on the positive numbers and the operators of Jacobi orthogonal system on (0,\pi). Okayasu investigated the structure of isometries on a function space and the Korovkin type linear approximation of them by contractions. Besides, he investigated the maximum part of a tuple of operators on a Hilbert space for which an indicated operator inequality holds. Mori researched about a problem of constructions of algebraically nondegenerate meromorphic mappings f of complex spaces C^m into complex projective spaces P^n(C) that for any given hypersurface D in P^n(C), f has the prescribed deficient value for D. Mizuhra showed the weak factorization theorem of H^1-functions due to Morrey functions, blocks and the Riesz potential. Also applying this result, we observed the necessity for which the commutator between the Riesz potential and a locally integrable function to be bounded on Morrey Spaces. Nakada studied some geometric properties of the Julia set of rational functions on the Riemann sphere. In particular, it is concerned with the group of euclidean motions which keep invariant the Julia set. Kawamura discussed an generalization of the theory concerning the behavior of probability density functions associated with chaotic maps on a measure space. The spaces he considered were AL and AM spaces and he generalized a convergence theory of probability density functions. Sekigawa examined some examples of transformations with torsion acting on the 3-dimensional Euclidean space by using Clifford matrix representations of M\" obius transformation.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] E.Sato: "Lorentz multipliers for Hankel transforms"Scientiae mathematicae Japonicae. 59(to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Okayasu: "Canonical decomposition of tuples of operators caused by systems of operator inequalities"Sci.Math.Jap. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Okayasu: "Canonical decomposition of operators caused by given operator inequalities"Trends in Math.. 6. 99-104 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Okayasu: "Some theorems of Korovkin type"Studia Math.. 155. 131-143 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Okayasu: "On essentially definite, and semidefinite tuples of operators"Sci.Math.Jap.. 56. 107-113 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Okayasu: "Estimates for moduli of coefficients of positive trigonometric polynomials"Sci.Math.Jap.. 56. 115-122 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Mori: "Meromorphic mappings and deficiencies"Advanced Studies in Pure Math., Complex Analysis is Several Variables.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.komori: "Notes on commutators and Morrey spaces"Hokkaido Math.J.. 32. 345-353 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] E.Sato: "Lorentz multipliers for Hankel transforms"Science mathematicae Japonicae. Vol.59,No.3(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Okayasu, Y.Ueta: "Canonical decomposition of tuples of operators caused by systems of operator inequalities"Sci.Math.Jap.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Okayasu, Y.Ueta: "Canonical decomposition of operators caused by given operator inequalities"Trends in Math.. 6(2). 99-104 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Okayasu, T.Hachiro: "Some theorems of Korovkin type"Studia Math.. 155(2). 131-143 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Okayasu, Y.Ueta: "On essentially definite, and semidefinite tuples of operators"Sci.Math.Jap.. 56(1). 107-113 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Okayasu, Y.Ueta: "Estimates for moduli of coefficients of positive trigonometric polynomials"Sci.Math.Jap.. 56(1). 115-112 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Mori: "Meromorphic mappings and deficiencies"Advanced Studies in Pure Mathematics, Complex Analysis in Several Variables. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Komori, T.Mizuhara: "Notes on Commutators and Morrey spaces"Hokkaido Math.J.. VOl.32. 345-353 (2003)

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

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Published: 2005-04-19  

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