Study of the boundary of numerrical range of Hilbert or Krein space operators and its applications

Hilbert或Kerin空间算子数值范围的边界研究及其应用

• 批准号: 23540180
• 负责人: NAKAZATO Hiroshi
• 金额: $ 1万
• 依托单位: Hirosaki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540180/
• 关键词: 数域; 数域半径; ヒルベルト空間; クレイン空間; 線形作用素; 行列; 固有値; シフト行列; 境界; 凸性; 作用素; 作用素の数域; 中心力

Some interesting results are found on the boundary of numerical range of linear operators in a finite dimensional Hilbert space. Especially some algebraic curve theoretic analysis is performed for shift operators. Concerning with Krein space numerical ranges, some results on the product ranges are obtained. The result will contribute to the basis of applications in nuclear magnetic resonance or spectral scopy. The results are presented in 16 academic papers and one book. By 7 presentations, the results are presented. New results in dynamics and hyperbolic differential equations are also obtained.

在有限维Hilbert空间中线性算子数值域的边界上得到了一些有趣的结果。特别是对移位算子进行了代数曲线理论分析。在Krein空间数值域方面，得到了乘积域的一些结果.这一结果将有助于在核磁共振或光谱学中的应用基础。结果发表在16篇学术论文和一本书中。通过7个演示，介绍了结果。在动力学和双曲型微分方程中也得到了新的结果。

项目成果

Textos de Mathematica

数学文本

• 发表时间: 2013
• 作者: Hiroshi Nakazato;Alexander Koacec;Natalia Bebiano
• 通讯作者: Natalia Bebiano

Hyperbolic forms associated with cyclic weighted shift matrices

与循环加权移位矩阵相关的双曲形式

• 发表时间: 2013
• 期刊: Linear Algebra and Its Applications
• 影响因子: 1.1
• 作者: Mao-Ting Chien;Hiroshi Nakazato
• 通讯作者: Hiroshi Nakazato

Construction of determinantal representations ..

行列式表示的构建..

• 发表时间: 2011
• 期刊: Linear Algebra and Its Applications
• 影响因子: 1.1
• 作者: Mao-Ting Chien;Hiroshi Nakazato
• 通讯作者: Hiroshi Nakazato

The main diagonal produuct of 3x3 normal matrices wihose eigenvalues are the third roots of unity

特征值是三次单位根的 3x3 正规矩阵的主对角积

• 发表时间: 2013
• 作者: H. Nakazato;A. Kovacec;N. Bebiano;P. da Providencia
• 通讯作者: P. da Providencia

Textos de mathematica, 44

数学文本，44

• 发表时间: 2013
• 作者: N. Bebiano;H. Nakazato el al
• 通讯作者: H. Nakazato el al