臺灣博碩士論文加值系統

由於古典:Nevanlinna-Pick:定理(Classical Nevanlinna-Pick Theorem) 在控制理論上扮演著十分重要角色，在此整理並介紹三種對此定理值得一看的的證明。進一步由矩陣頻譜半徑的插值問題 (Spectral Nevanlinna-Pick Problem) 討論一些對稱雙盤 (symmetrized bidis)上的插值問題及相關性質，並計算對稱雙盤(參)圓的體積及表面積，並提供對稱多盤 (symmetrized n-disc) 體積求法的積分形式。

Because The classical Nevanlinna-Pick Theorem plays a very important role in the robust control theory, we like to introduce three worth-reading proofs of the theorem. Furthermore we will develop into the area of spectral Nevanlinna-Pick problem: discuss some interpolation problems and properties on the symmetrized-bidisc , and calculate the volume and surface area of symmetrized-bidisc and symmetrized-tridisc, and gives the general integral form to represent the volume of symmetrized-n-disc.

Chinese abstract i
Abstract ii
Notations iii
Contents v
Chapter 1 Introduction
1.1 From Robust control to Nevanlinna-Pick problem 1
1.2 Motivation and organization 4
Chapter 2 Preliminaries
2.1 Basic preliminaries 5
2.2 Preliminaries about function analysis 7
2.3 Preliminaries about spectral Nevanlinna-Pick problem and Γn 14
Chapter 3 Main results
3.1 Three worth-reading proofs of Nevanlinna-Pick Theorem 24
3.1.1 A Proof with Fenyers array 24
3.1.1 A Proof from Donald E. Marshall 32
3.1.1 A Proof from J. R. Partington 36
3.2 Remarks on the propertities of Γn and some interpolation problem 38
3.2.1 Remarks on the propertities of Γn 38
3.2.1 N points interpolation problem 42
3.3 The Volume and Surface Area of Symmetrized Polydiscs 45
Chapter 4 Conclusion 50
Reference 51

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