| 研究生: |
李建杰 Chien-Chieh Lee |
|---|---|
| 論文名稱: |
格瑪算子函數的應用 An Application of Gamma Operator Functions |
| 指導教授: | 李源泉 |
| 口試委員: | |
| 學位類別: |
碩士 Master |
| 系所名稱: |
理學院 - 數學系 Department of Mathematics |
| 畢業學年度: | 91 |
| 語文別: | 英文 |
| 論文頁數: | 16 |
| 外文關鍵詞: | Gamma operator function, Fractional powers |
| 相關次數: | 點閱:17 下載:0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本篇論文主要是定義格瑪算子函數, 並且藉由我們所定義的格瑪算子函數,
建構一個單變數半群的極小生成的分數冪次, 並且得到一些關於格瑪
算子函數的定理.
1. A. V. Balakrishnan, Fractional powers of closed operators and the semi-groups generated
by them, Pacific J. Math. 10(1960)419-437.
2. E. B. Davies, ONE-PARAMETER SEMIGROUPS, ACADEMIC PRESS, 1980.
3. Leopold Flatto, Advanced Calculus, reprinted by MEI YA PUBLICATIONS Inc. Taipei,
Taiwan.(1976)415-424.
4. Jerme A. Goldstein, Semigroups of Linear Operators and Applications, New York Oxford
University press 1985.
5. T. Kato, Fractional powers of dissipative operators, J. Math. soc. Japan 13(1961)246-
274.
6. T. Kato, Fractional powers of dissipative operators II, J. Math. soc. Japan 14(1962)242-
248.
7. H. Komatsu, Fractional powers of operators, Pacific J. Math. 19(1966)285-346.
8. H. Komatsu, Fractional powers of operators II Interpolation space, Pacific J. Math.
21(1967)89-111.
9. H. Komatsu, Fractional powers of operators III Negative powers, J. Math. Soc. 21(1969)205-
220.
10. H. Komatsu, Fractional powers of operators IV Potential operators, J. Math. Soc.
21(1969)221-228.
11. H. Komatsu, Fractional powers of operators V Dual operators, J. Fac. Sc. Univ of Tokyo
17(1970)373-396.
12. A. Pazy, Semigroups of Linear Operators and Applications to Partial Di erential Equations,
Springer-Verlag, NEW YORK Inc.(1983).
13. Murray R. Spiegel, Advanced Calculus, reprinted by CHAUM PUBLICATIONS Inc.
NEW YORK.(1963)286.
14. K. Yosida, Functional analysis, Springer-Verlag Berlin Heidelberg New York 6ed, 1980.