Functional Analysis

S Kesavan

ISBN 10: 9380250622 / ISBN 13: 9789380250625

Published by Hindustan Book Agency, 2009

About this Item

Contents 1. Preliminaries. 2. Normed linear spaces. 3. Hahn Banach theorems. 4. Baire's theorem and applications. 5. Weak and weak topologies. 6. Lp spaces. 7. Hilbert spaces. 8. Compact operators. Bibliography. Index. The material presented in this book is suited for a first course in Functional Analysis which can be followed by masters students. While covering all the standards material expected of such a course efforts have been made to illustrate the use of various theorems via examples taken from differential equations and the calculus of variations either through brief sections or through exercises. In fact this book will be particularly useful for students who would like to pursue a research career in the applications of mathematics. The book includes a chapter on weak and weak topologies and their applications to the notions of reflexivity separability and uniform convexity. The chapter on the Lebesgue spaces also presents the theory of one of the simplest classes of Sobolev spaces. The book includes a chapter on compact operators and the spectral theory for compact self adjoint operators on a Hilbert space. Each chapter has large collection of exercises at the end. These illustrate the results of the text show the optimality of the hypotheses of various theorems via examples or counterexamples or develop simple versions of theories not elaborated upon in the text. 269 pp.

Seller Inventory # 73665

Bibliographic Details

• Title: Functional Analysis
• Publisher: Hindustan Book Agency
• Publication Date: 2009
• Language: English
• ISBN 10: 9380250622
• ISBN 13: 9789380250625
• Binding: Soft cover
• Condition: New

About this title

Synopsis

The material presented in this book is suited for a first course in Functional Analysis which can be followed by masters students. While covering all the standard material expected of such a course, efforts have been made to illustrate the use of various theorems via examples taken from differential equations and the calculus of variations, either through brief sections or through exercises. In fact, this book will be particularly useful for students who would like to pursue a research career in the applications of mathematics. The book includes a chapter on weak and weak*topologies and their applications to the notions of reflexivity, separability and uniform convexity. The chapter on the Lebesgue spaces also presents the theory of one of the simplest classes of Sobolev spaces. The book includes a chapter on compact operators and the spectral theory for compact self-adjoint operators on a Hilbert space. Each chapter has large collection of exercises at the end. These illustrate the results of the text, show the optimality of the hypotheses of various theorems via examples or counterexamples, or develop simple versions of theories not elaborated upon in the text.