| Abstract: | 考慮symmetrized bidisc $\Gamma_{2}$：% $$\Gamma_{2}\triangleq \{(s,p):\lambda^{2}-s\lambda+p=0,~\lambda \in \mathbb{C},~|\lambda|\leq1\}$$% 定義其上的 spectral Nevanlinna-Pick 插值非平問題({\rm Int}erpolation non-flat problem)為：\\ % 給定$\alpha_{1},~\alpha_{2} \in \mathbb{D},~(s_{1},0),~(s_{2},0) % \in {\rm Int}~\Gamma_{2} $，% $\varphi : \mathbb{D} \longrightarrow {\rm Int}~\Gamma_{2}$，為解析函數，% 使得~$\varphi(\alpha_{1}) = (s_{1},0)$，$\varphi(\alpha_{2}) = (s_{2},~0)$，% 藉由Carath$\acute{e}$odory 距離與Kobayashi距離相等的假設下，% 利用Schur定理，吾人建構出滿足此問題的解析函數$\varphi$。
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. |
