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Operator theoretical study of inverse problems in linear systems

Research Project

Project/Area Number 07640155
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionNagoya Institute of Technology (1996)
Hokkaido University (1995)

Principal Investigator

NAKAMURA Yoshihiro  Nagoya Institute of Technology, Faculty of Engineering, Assistant Professor, 工学部, 助教授 (50155868)

Co-Investigator(Kenkyū-buntansha) OHYAMA Yoshiyuki  Nagoya Institute of Technology, Faculty of Engineering, Assistant Professor, 工学部, 助教授 (80223981)
ADACHI Toshiaki  Nagoya Institute of Technology, Faculty of Engineering, Assistant Professor, 工学部, 助教授 (60191855)
YOSIMURA Zenichi  Nagoya Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (70047330)
NAKAI Mitsuru  Nagoya Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (10022550)
TODA Nobushige  Nagoya Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (30004295)
安藤 毅  北星学園大学, 経済学部, 教授 (10001679)
高橋 勝利  北海道大学, 大学院・理学研究科, 助教授 (60133774)
中路 貴彦  北海道大学, 大学院・理学研究科, 教授 (30002174)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1996: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1995: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordslinear system / operator / Hilbert space / indefinite inner product / interpolation / 伝達関数 / z-変換 / Hadamard積 / マジョリゼーション
Research Abstract

Nakamura investigated an inverse problem in the time-varying linear system according to the models of contractions and J-contractions on Hilbert spaces and indefinite inner product spaces, respectively, which are developed by de Branges and Rovnyak. Also he studied a method of constructing the lossless linear system by a given scattering matrix.
The backward shift, which is the adjoint operator of the unilateral shift operator, is a most basic linear operator in the operator models of linear systems. When the backward shift acts on a de Branges-Rovnyak space, it is a expansive operator and unitarily equivalent to a one-dimensional perturbation of the shift operator. According to this fact he investigated expansive operators which are one-dimensional perturbation of the shift operator in full detail and obtained conditions for those operators to be similar or quasisimilar to the shift operator. Further spectra and invariant subspaces of those operators were described explicitly.
Nakamura also investigated the inequality of Popoviciu from a view point of a variation of the Cauchy-Schwarz inequality in an indefinite inner product form, and gave a new transparent proof of the inequality. As it's application the inequality of Bellman was proved clearly.
Toda and Nakai advanced the research from a view point of Complex Analysis, and obtained results on subsets of C^<n+1> in general position and Brelot spaces of Schrodinger equations.
Yosimura and Ohyama advanced the research from a view point of Topology, and obtained results on the K_<**>-local types of the smash product of the real projective spaces and Vassiliev invariants in Knot Theory.
Adachi advanced the research from a view point of Differential Topology, and obtained a results on circles on a quaternionic space form.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (21 results)

All Other

All Publications (21 results)

  • [Publications] T.Adachi: "Circles on a quaternionic space form" J. Math. Soc. Japan. 48・2. 205-227 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Nakai: "Brelot spaces of Schrodinger equations" J. Math. Soc. Japan. 48・2. 275-298 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y.Ohyama: "Twisting of two strings and Vassiliev invariants" Topology and its Applications. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] A.Saeki: "On some foliations on ruled surfaces of genus one" Kumamoto J. Math.9・1. 45-52 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N.Toda: "On subsets of C^<n+1> in general position" Proc. Japan Acad., Ser. A. 72・3. 55-58 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Z.Yosimura: "The K_*-local types of the smash product of the real projective spaces" Hiroshima Math. J.26. 301-321 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Adachi: "Circles on a quaternionic space form" J.Math.Soc.Japan. 48-2. 205-227 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Nakai: "Brelot spaces of Schrodinger equations" J.Math.Soc.Japan. 48-2. 275-298 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y.Ohyama: "Twisting of two strings and Vassiliev invariants" Topology and its Applications. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] A.Saeki: "On some foliations on ruled surfaces of genus one" Kumamoto J.Math.9-1. 45-52 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N.Toda: "On subsets of C^<n+1> in general position" Proc.Japan Acad., Ser.A. 72-3. 55-58 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Z.Yosimura: "The K_<**>-local types of the smash product of the real projective spaces" Hiroshima Math.J.26-2. 301-321 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Adachi: "Circles on a quaternionic space form" J.Math.Soc.Japan. 48・2. 205-227 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Nakai: "Brelot spaces of Schrodinger equations" J.Math.Soc.Japan. 48・2. 275-298 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Ohyama: "Twisting of two strings and Vassiliev invariants" Topology and its Applications. (印刷中).

    • Related Report
      1996 Annual Research Report
  • [Publications] A.Saeki: "On some foliations on ruled surfaces of genus one" Kumamoto J.Math.9・1. 45-52 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] N.Toda: "On subsets of C^<n+1> in general position" Proc.Japan Acad.,Ser.A. 72・3. 55-58 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Z.Yosimura: "The K_*-local types of the smash product of the real projective spaces" Hiroshima Math.J.26. 301-321 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 中村美浩: "時変システムの合成と非可換z変換について" ディジタル信号処理シンポジウム講演論文集. 10. 25-29 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Ando: "Majorization relations for Hadamard products" Limear Algelera Appl.223/224. 57-64 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Ando: "Extreme points of an intersection of operator intervals" Proc.Intermat.Math.Conf.1-18 (1996)

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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