臺灣博碩士論文加值系統

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.

1 簡介
1.1 符號
1.2 $\mu$-設計理論
2 數學預備知識
2.1 強韌穩定性與強韌性能
2.2 Nevanlinna-Pick 插值問題
2.3 Spectral Nevanlinna-Pick 問題
2.4 $\Gamma_{2}$上的距離問題
3 主要想法與結果
3.1 $\Gamma_{2}$上的一些性質
3.2 的充分條件與必要條件
3.3 的建立方式
3.4 二維之實現
4 結論與展望

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