請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/68856完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蕭欽玉(Chin-Yu Hsiao) | |
| dc.contributor.author | Nai-Yo Hu | en |
| dc.contributor.author | 胡乃友 | zh_TW |
| dc.date.accessioned | 2021-06-17T02:38:50Z | - |
| dc.date.available | 2020-08-25 | |
| dc.date.copyright | 2017-08-25 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-08-16 | |
| dc.identifier.citation | {1}R. Strichartz, A Guide To Distribution Theory and Fourier Transforms. Boca Raton, FL: CRC Press, 1994.
{2}Daniel Grieser, Notes on heat kernel asymptotics. Preprint, Available at http://www.staff.unioldenburg.de/daniel.grieser/wwwvortraege/vortraege.html. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/68856 | - |
| dc.description.abstract | 在這篇文章中，我們研究關於在歐氏空間中薛丁格算子的熱核的表現式與它的漸近展開。先從觀察簡單的常係數薛丁格算子在歐氏空間中的行為開始，並引入新的符號空間，由逼近的方法將熱核的表現式寫下來。從而證明在歐氏空間中薛丁格算子的熱核的存在唯一性，並得到其在時間趨近於零時的漸進展開。 | zh_TW |
| dc.description.abstract | In this thesis, we study the expression of the heat kernel of the Schrodinger operator in Euclidean space and its asymptotic expansion. We start by observing the behavior of the constant coefficient Schr'odinger operator in Euclidean space and introduce the new symbol space, and write down the expression of the heat kernel by the approximation method. It's proved the existence and uniqueness of the heat kernel for the Schr'odinger operator in Euclidean space, and the asymptotic expansion of the heat kernel at time is approach to 0. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T02:38:50Z (GMT). No. of bitstreams: 1 ntu-106-R04221007-1.pdf: 544479 bytes, checksum: 929a9319f9d7a3cc32de5007eefca7f1 (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 中文摘要2
Abstract 3 1. Introduction 1 1.1. Basic Schr odinger operator 1 1.2. General Heat operator 1 2. Basic Schr odinger operator 3 3. General Heat operator 7 3.1. Outline of the proof of Theorem 1.1 7 3.2. Symbol space and convolution product 7 3.3. The Volterra series 14 3.4. Proof of Theorem 1.1 17 References 19 | |
| dc.language.iso | en | |
| dc.subject | 薛丁格算子 | zh_TW |
| dc.subject | 漸進展開 | zh_TW |
| dc.subject | 符號空間 | zh_TW |
| dc.subject | 熱核 | zh_TW |
| dc.subject | asymptotic expansion | en |
| dc.subject | symbol space | en |
| dc.subject | heat kernel | en |
| dc.subject | Schrodinger operator | en |
| dc.title | 在歐氏空間上薛丁格算子的熱核漸進展開 | zh_TW |
| dc.title | Heat kernel asymptotic expansions for Schrödinger operator on R^n | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃榮宗,鄭日新 | |
| dc.subject.keyword | 薛丁格算子,熱核,漸進展開,符號空間, | zh_TW |
| dc.subject.keyword | Schrodinger operator,heat kernel,asymptotic expansion,symbol space, | en |
| dc.relation.page | 19 | |
| dc.identifier.doi | 10.6342/NTU201703644 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2017-08-17 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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