Spectral Nevanlinna-Pick Interpolation On Symmetrized Bidisc

• Main Authors: Tien-De Lin, 林天得
• Other Authors: Fang-Bo Yeh
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/94495204389019542431

碩士 === 東海大學 === 數學系 === 89 === Consider symmetrized bidisc $\Gamma_{2}$:% $$\Gamma_{2}\triangleq \{(s,p):\lambda^{2}-s\lambda+p=0,~\lambda \in \mathbb{C},~|\lambda|\leq1\}$$% and spectral Nevanlinna-Pick Interpolation non-flat problem on it as:\\ % Given $\alpha_{1},~\alpha_{2} \in \mathbb{D},~(s_{1},0),~(s_{2},0) % \in {\rm Int}~\Gamma_{2} $,% $\varphi : \mathbb{D} \longrightarrow {\rm Int}~\Gamma_{2}$,is analytic,% ~such that~$\varphi(\alpha_{1}) = (s_{1},0)$，$\varphi(\alpha_{2}) = (s_{2},~0)$,% ~by the equality of Carath$\acute{e}$odory and Kobayashi distances,% ~and Schur theorem, ~we can find $\varphi$ that we want.