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

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。

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.