Intended as an introductory text on Functional Analysis for the postgraduate students of Mathematics, this compact and well-organized book covers all the topics considered essential to the subject. In so doing, it provides a very good understanding of the subject to the reader.
The book begins with a review of linear algebra, and then it goes on to give the basic notion of a norm on linear space (proving thereby most of the basic results), progresses gradually, dealing with operators, and proves some of the basic theorems of Functional Analysis. Besides, the book analyzes more advanced topics like dual space considerations, compact operators, and spectral theory of Banach and Hilbert space operators. The text is so organized that it strives, particularly in the last chapter, to apply and relate the basic theorems to problems which arise while solving operator equations.
The present edition is a thoroughly revised version of its first edition, which also includes a section on Hahn-Banach extension theorem for operators and discussions on Lax-Milgram theorem.
This student-friendly text, with its clear exposition of concepts, should prove to be a boon to the beginner aspiring to have an insight into Functional Analysis.
KEY FEATURES
• Plenty of examples have been worked out in detail, which not only illustrate a particular result, but also point towards its limitations so that subsequent stronger results follow.
• Exercises, which are designed to aid understanding and to promote mastery of the subject, are interspersed throughout the text.
TARGET AUDIENCE
• M.Sc. Mathematics
Dr. M. THAMBAN NAIR is a Professor of Mathematics at the Indian Institute of Technology Madras, Chennai. He obtained Ph.D from Indian Institute of Technology Bombay and was a Post Doctoral Fellow at the University of Grenoble (France) under the French Government Fellowship. He has held visiting positions at the Australian National University, Canberra (Australia), University of Kaiserslautern (Germany), Sun Yat-sen University, Guangzhou (China), University of Saint-Etienne (France), Weierstrass Institute for Applied Analysis and Stochastics, Berlin (Germany). Besides, he has given many invited talks at various institutes in India and abroad. A vigorous researcher in the area of applicable functional analysis, Dr. Nair has published over 75 research papers in nationally and internationally reputed journals. He has authored three more books, Linear Operator Equations: Approximation and Regularization, Calculus of One Variable, Measure and Integration: A First Course and also co-authored a book Linear Algebra. Dr. Nair has received many awards for his academic achievements, including the C.L. Chandna Award of the Indo-Canadian Mathematics Foundation for outstanding contributions in mathematics research and teaching for the year 2003.
