- 學位論文
一個廣義Ornstein-Uhlenbeck的熱核
Heat Kernel for a Generalized Ornstein-Uhlenbeck operator
摘要
在這篇文章，我們使用漢米爾頓與拉格朗日形式來研究這個二 維廣義Ornstein-Uhlenbeck 算子 給定邊界條件後，我們解出這個算子所對應的漢米爾頓系統。然後 利用拉格朗日函數來建構動能函數，利用范夫來克公式得到熱核的 量能項。最後，我們討論此算子的正則與奇異區域。
關鍵字
熱核並列摘要
In this thesis, we use the Hamiltonian and Lagrangian formalism to study the two-dimensional generalized Ornstein-Uhlenbeck operator Given the boundary conditions, we find the solutions of the associated Hamiltonian system of this operator. Then we construct the action function by the Lagrangian function and use the van Vleck's formula to obtain the volume element of the heat kernel. Finally, we discuss the regular and singular regions of this operator.
並列關鍵字
Heat Kernel參考文獻
[1] Der-Chen Chang and Luping Chen, Initial value problem and the heat
[3] Der-Chen Chang and Sheng-Ya Feng, Geometric analysis on generalized
[8] R. Beals, A note on fundamental solutions. Comm. Partial Dierential
fundamental solution of subelliptic Laplacians. Math. Nachr. 181, 81-163.
kernel for a mixed type operators.
延伸閱讀
- Yu, S. H. (2015). 完備流形上熱核的梯度估計 [master's thesis, National Tsing Hua University]. Airiti Library. https://doi.org/10.6843/NTHU.2015.00183
- 孔令鈞 (2011). 一個更普遍用於半經典理論研究化學反應動態學的絕熱勢能曲線 [master's thesis, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2011.01153
- Chen, B. J. (2022). 熱輔助密度泛函理論由一簡單模型賦予虛擬溫度物理意義以及演示混和泛函對此計算方法之重要性 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU202200170
- 劉之昀（2013）。雙分佈函數半古典格子波茲曼法之熱流場模擬〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2013.00116
- 張丁中（2011）。The Kernel Estimator of The Median〔碩士論文，國立中央大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0031-1903201314415616