Functional Analysis

  • S. Kesavan

Part of the Texts and Readings in Mathematics book series (TRM, volume 52)

Table of contents

  1. Front Matter
    Pages i-xii
  2. S. Kesavan
    Pages 1-25
  3. S. Kesavan
    Pages 26-68
  4. S. Kesavan
    Pages 69-96
  5. S. Kesavan
    Pages 97-131
  6. S. Kesavan
    Pages 132-161
  7. S. Kesavan
    Pages 162-194
  8. S. Kesavan
    Pages 195-230
  9. S. Kesavan
    Pages 231-264
  10. Back Matter
    Pages 265-272

About this book


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.

Authors and affiliations

  • S. Kesavan
    • 1
  1. 1.Institute of Mathematical SciencesChennaiIndia

Bibliographic information