Project/Area Number  07640155 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

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

CoInvestigator(Kenkyūbuntansha) 
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)
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)
TODA Nobushige Nagoya Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (10022550)
NAKAI Mitsuru Nagoya Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (30004295)

Project Fiscal Year 
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)

Keywords  linear system / operator / Hilbert space / indefinite inner product / interpolation / 線形システム / 作用素 / ヒルベルト空間 / 不定内積空間 / 補間理論 / 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 timevarying linear system according to the models of contractions and Jcontractions 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 BrangesRovnyak space, it is a expansive operator and unitarily equivalent to a onedimensional perturbation of the shift operator. According to this fact he investigated expansive operators which are onedimensional 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 CauchySchwarz 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.
