関数解析と作用素論の応用（第２版） Applications of Functional Analysis and Operator Theory: Volume 200 (Mathematics in Science and Engineering") 〈200〉 （2ND）

Hutson, V./ Pym, J./ Cloud, M.

Elsevier Science（2005/03発売）

• 製本 Hardcover:ハードカバー版／ページ数 432 p.
• 言語 ENG
• 商品コード 9780444517906
• DDC分類 515.7

基本説明

２５年振りの改訂版。
Provides an ideal transition between introductory math courses and advanced graduate study. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations).

Full Description

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.

Contents

1. Banach Spaces2. Lebesgue Integration and the Lp Spaces3. Foundations of Linear Operator Theory4. Introduction to Nonlinear Operators5. Compact Sets in Banach Spaces6. The Adjoint Operator7. Linear Compact Operators8. Nonlinear Compact Operators and Monotonicity9. The Spectral Theorem10. Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations11. Linear Elliptic Partial Differential Equations12. The Finite Element Method13. Introduction to Degree Theory14. Bifurcation Theory