Mendeley出力
＜図書＞
Lectures on functional analysis and applications
| 責任表示 | V.S. Pugachev & I.N. Sinitsyn ; translated by I.V. Sinitsyna |
|---|---|
| データ種別 | 図書 |
| 出版情報 | Singapore ; River Edge, NJ : World Scientific , c1999 |
| 本文言語 | 英語 |
| 大きさ | xx, 730 p. : ill. ; 23 cm |
| 概要 | The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general...case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric. To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc. The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric. To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc. 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 |
|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
理系図3F 数理独自 | PUGA/10/5 | 1999 |
|
023211999005018 |
|
|||
|
|
|
芸工図 2F 書架 | 415.5/P96 | 1999 |
|
072032199006063 |
|
書誌詳細
| 一般注記 | Includes bibliographical references (p. 719-722) and index |
|---|---|
| 著者標目 | *Pugachev, V. S. (Vladimir Semenovich) Sinit︠s︡yn, I. N. (Igorʹ Nikolaevich) |
| 件 名 | LCSH:Functional analysis |
| 分 類 | LCC:QA320 DC21:515/.7 |
| 書誌ID | 1000924678 |
| ISBN | 9810237227 |
| NCID | BA42666276 |
| 巻冊次 | ISBN:9810237227 : pbk ; ISBN:9810237235 |
| 登録日 | 2009.09.16 |
| 更新日 | 2009.11.02 |