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Functional Analysis
S. Kesavan, Institute of Mathematical Sciences, Chennai, India
A publication of Hindustan Book Agency.
Hindustan Book Agency
2009; 281 pp; hardcover
ISBN-10: 81-85931-87-9
ISBN-13: 978-81-85931-87-6
List Price: US$44
Member Price: US$35.20
Order Code: HIN/39
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The material presented in this book is suited for a first course in Functional Analysis which can be followed by master's students. While all the standard material expected of such a course is covered, 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 on in the text.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students interested in functional analysis.

Table of Contents

  • Preliminaries
  • Normed linear spaces
  • Hahn-Banach theorems
  • Baire's theorem and applications
  • Weak and weak* topologies
  • \(L^p\) spaces
  • Hilbert spaces
  • Compact operators
  • Bibliography
  • Index
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