Functional Analysis

Functional Analysis is based on the lecture notes of distinguished authors and is designed to cater to the needs of students who are yet to be exposed to the subject, as well as senior undergraduate- and graduate-level students at universities the world over.

The text begins with a preliminary chapter that establishes uniform notations and covers background material in real analysis, linear algebra, and metric spaces. It is followed by chapters on Normed and Banach Spaces, Bounded Linear Operators and Bounded Linear Functionals. This text also deals with the concept and specific geometry of Hilbert Spaces, Functionals and Operators on Hilbert Spaces, and an Introduction to Spectral Theory. The appendix provides an introduction to Schauder Bases.

P K Jain, Fellow of the National Academy of Sciences (F.N.A.Sc.); Emeritus Fellow (U.G.C.) and formerly, Professor and Head, Department of Mathematics, University of Delhi, having teaching and research experience of 43 years, has published 130 research papers and 12 expository articles in the areas of Complex Analysis, Functional Analysis, Sobolev Spaces, Hardy-type Inequalities and Operators, Theory of Frames.

O P Ahuja, M.Sc., M.A., Ph.D., recipient of 30 international recognitions and funded grants, including the National Science Foundation Grant (USA, 2005) and two times nominee of the `US Professors of the Year Award` (2005, 2006); currently serves as an Associate Professor of Mathematics at Kent State University in Ohio, USA. He has taught at many international institutions including the University of California (Davis), Nanyang Technological University in Singapore, University of Khartoum in Sudan, and the University of Addis Ababa in Ethiopia. Dr. Ahuja`s research interests include complex analysis, functional analysis, and mathematics education. He has contributed over 100 papers to mathematics and mathematics education journals and has served as a reviewer for the American Mathematical Society for the past 25 years.