Mendeley出力
＜図書＞
Pseudo-differential operators
| 責任表示 | Hitoshi Kumano-go ; [translated by Hitoshi Kumano-go, Rémi Vaillancourt, and Michihiro Nagase] |
|---|---|
| データ種別 | 図書 |
| 出版者 | Cambridge, Mass. : MIT Press |
| 出版年 | c1981 |
| 本文言語 | 英語 |
| 大きさ | xviii, 455 p. : ill. ; 24 cm |
| 概要 | This self-contained and formal exposition of the theory and applications of pseudo-differential operators is addressed not only to specialists and graduate students but to advanced undergraduates as w...ll. The only prerequisite is a solid background in calculus, with all further preparation for the study of the subject provided by the book's first chapter. This chapter introduces the fundamental concepts of spaces of functions and Fourier transforms, and covers such topics as linear operators, linear functionals, dual spaces, Hilbert spaces, distributions, and oscillatory integrals. The second chapter develops the theory of pseudo-differential operators themselves on the basis of elementary calculus and concepts presented in the opening chapter, while the third chapter extends the theory of Sobolev spaces. The major applications of the theory, most of them the result of work done since 1965, are in the study and solution of linear partial differential equations, which are found in many branches of pure and applied mathematics and are ubiquitous throughout the sciences and technology. The final seven chapters of Pseudo-Differential Operators take up a range of applications, and deal with such problems as hypoellipticity, local solvability, local uniqueness, index theory, elliptic boundary values, complex powers, initial values, well-posedness, the fixed point theorem of Atiyah-Bott-Lefschetz, Fourier integral operators, and propagation of singularities. For this English edition, the last chapter has been greatly extended and appendixes added in order to present the latest developments of the subject. Multiphase Fourier integral operators are applied to initial-value problems, the micro-local theory is developed from the notion of the "wave front set," and the Nirenberg-Treves existence theorem for the solutions of partial differential equations is discussed. The systematic use of the "multiple symbols" introduced by K. O. Friedrichs provides elegant proofs of otherwise lengthy developments. Hitoshi Kumano-Go teaches in the Mathematics Department at Osaka University. 続きを見る |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
|---|---|---|---|---|---|---|---|---|---|---|
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理系図1F 開架 | 413.63/Ku 34 | 1981 |
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031212009000034 |
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理系図3F 数理独自 | KUMA/10/1A | 1981 |
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023212004500220 |
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理系図3F 数理独自 | KUMA/10/1 |
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068222183001631 |
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【故障中】理系図 自動書庫 | 104/KUM | 1981 |
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068252183010253 |
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書誌詳細
| 別書名 | 原タイトル:擬微分作用素 |
|---|---|
| 一般注記 | Updated translation of: 擬微分作用素. 1974 Bibliography: p. [421]-451 Includes index |
| 著者標目 | 熊ノ郷, 準(1935-) <クマノゴウ, ヒトシ> Vaillancourt, Rémi, 1934- 長瀬, 道弘 <ナガセ, ミチヒロ> |
| 件 名 | LCSH:Pseudodifferential operators |
| 分 類 | LCC:QA329.7 DC19:515.7/242 |
| 書誌ID | 1000046108 |
| ISBN | 0262110806 |
| NCID | BA00470325 |
| 巻冊次 | ISBN:0262110806 |
| 登録日 | 2009.09.10 |
| 更新日 | 2009.09.17 |