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姓名 劉翔( Xang Liu)  查詢紙本館藏   畢業系所 數學系
論文名稱 摺合型積分方程之收斂性,可微性與可容許空間的研究。
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摘要(中) 本文可分為兩個部份:第一個部份是探討Volterra 積分方程之預解算子族在原點的收斂性及參數可微性;第二個部份則研究摺合型積分方程的可容許空間與Lyapunov 算子方程的可解性之聯繫。
第二章給出了n次積分預解算子族的最佳與非最佳收斂及其敏銳,並將之應用於n次積分半群及n次積分餘弦函數。
在第三章中我們定義A規則逼近過程,並建立了決定其飽和度與飽和類之一般流程。應用此流程於n次積分預解算子族而得到第二章的一些結果。
第四章則研究Volterra 積分方程之參數可微性。在一些假設之下,我們證明了Volterra 積分方程解的參數可微性蘊含其預解算子族的參數可微性。
第五章首先給出了一類Lyapunov 算子方程有唯一解的充要條件。其次證明了摺合型積分方程之可容許空間與Lyapunov算子方程之可解性間的等價關係。最後給出摺合算子生成解析半群之充要條件,並引用一個已知的定理給出Lyapunov算子方程解的公式。
關鍵字(中) ★ 可容許空間
★ 預解算子族
★ 算子半群
關鍵字(英)
論文目次 封面
Chapter 1. Introduction
Chapter 2. Rates of Local Ergodic Limits of N-times Integrated Solution Families
Chapter 3. Convergence Rates of Regulized Approximation Process
Chapter 4. The Differentiablity with respect to a Parameter of the Solution of a Linear Abstract Volterra Equation
Chapter5 Admissible Spaces of Convolution Integral Equations and the Solvability of Operator Equations of Lyopunov Type
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指導教授 蕭勝彥(Sen-Yen Shaw) 審核日期 2001-6-27
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