This second edition is thoroughly revised and includes several new examples and exercises. Proofs of many results have been rewritten for a greater clarity. While covering all the standard material expected of such a course, efforts have been made to illustrate the use of the topics to study differential equations and calculus of variations. The book includes a chapter on weak topologies and their applications. It also includes a chapter on the Lebesgue spaces, which discusses Sobolev spaces. The book includes a chapter on compact operators and their spectra, especially for compact self-adjoint operators on a Hilbert space. Each chapter has a large collection of exercises in the end, which give additional examples and counterexamples to the results given in the text. This book is suitable for a first course in functional analysis for graduate students who wish to pursue a career in the applications of mathematics.
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ISBN-13
978-981-19-7633-9 (9789811976339)
DOI
10.1007/978-981-19-7633-9
Schweitzer Klassifikation
S. Kesavan is Adjunct Professor at the Indian Institute of Technology Madras, Chennai, India. He received his Docteur-es-Sciences Mathematiques from the Universite Pierre et Marie Curie (Paris VI) in 1979 for the thesis entitled "Sur l'approximation de probl`emes lineaires et nonlineaires de valeurs propres", supervised by Professors J.L. Lions and P.G. Ciarlet. Earlier, he was a Deputy Director of Chennai Mathematical Institute (CMI) during 2007-2010; TIFR Centre for Applicable Mathematics, Bengaluru, India. His research areas include partial differential equations, homogenization, control theory and isoperimetric inequalities.
Author of 5 books, Prof. Kesavan has published more than 50 papers in national and international journals and several contributions to conference proceedings. He was elected Vice-President of the Ramanujan Mathematical Society in 2016 (served from 2016-2019); Fellow of the Indian Academy of Sciences, Bengaluru; Fellow of the National Academy of Sciences, India; Member of the National Board of Higher Mathematics (NBHM) (from 2000-2019); and Secretary, Grants Selection; Commission for Developing Countries, International Mathematical Union (from 2011-2018). He is Recipient of the C.L. Chandna Award for Outstanding Contributions to Mathematics Research and Teaching (1999) and Tamil Nadu Scientist Award, awarded by the Tamil Nadu State Council for Science and Technology, in Mathematical Sciences (1998).
Preliminaries.- Normed Linear Spaces.- Hahn-Banach Theorems.- Baire's Theorem and Applications.- Weak and Weak* Topologies.-
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Spaces.- Hilbert Spaces.- Compact Operators.
