Description

FUNCTIONAL ANALYSIS

This book is an introductory text written with minimal prerequisites. The plan is to impose a distance structure on a linear space, exploit it fully, and then introduce additional features one by one, only when we cannot get any further without them. The book naturally falls into two parts, and each of them is developed independently of the other. The first part deals with normed spaces, their completeness and continuous linear maps on them, and includes the theory of compact operators. A much shorter second part treats inner product spaces, their completeness, and leads to the spectral theorem for compact self-adjoint operators. Four appendices on Fixed Points, Extreme Points.

Sturm-Liouville Problems and Unbounded Operators indicate further areas of development.

Emphasis is given on examples which illustrate abstract concepts, and on applications of results proved in the text. In addition to proving existence and uniqueness of the solution of a problem, an approximate construction of the solution is pointed out.

Problems of varying degrees of difficulty are given at the end of each of the sections in Chapter II to VII. The statement of each problem contains its answer.

Balmohan V Limaye is Professor Emeritus at the Indian Institute of Technology Bombay, Mumbai. After completing his doctorate at the University of Rochester, New York, he taught at the University of California, Irvine. He was a member of the Schoolof Mathematics of the Tata Institute of Fundamental Research, Mumbai. Later he worked at the Indian Institute of Technology Bombay for 42 years. Professor Limaye has published numerous research articles in the areas of algebraic analysis, projective geometry, numerical functional analysis and linear algebra. He is a coauthor of two undergraduate textbooks on Calculus and Analysis and two research monographs entitled Real Function Algebras and Spectral Computations for Bounded Operators.

Readership: Undergraduate/postgraduate students and Faculty members of colleges, universities and similar institutes • Researchers and professionals.

Pages: 612