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List of contents
Preface. Note to the Reader. Review of Riemann Integral. Lebesgue Measure. Measure and Measurable Functions. Integral of Positive Measurable Functions. Integral of Complex Measurable Functions. Integration on Product Spaces. Fourier Transform. References. Index.
About the author
M Thamban Nair is a Professor of Mathematics at the Indian Institute of Technology Madras, Chennai, India. After completing his Ph.D. thesis in 1984 from the Indian Institute of Technology Bombay, Mumbai (India), he did his post-doctoral research at the University of Grenoble (France), for a year under a French Government Scholarship, and after returning from France, he worked as a Research Scientist at Indian Institute of Technology Bombay for a year. He taught at the Goa University almost for a decade, and from December 1995 onwards, he is a regular faculty member at the Indian Institute of Technology Madras. He 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), and University of Chemnitz (Germany). Besides, he has given many invited talks at various institutes in India and abroad.
The broad area of Professor Nair’s research is in Functional Analysis and Operator Theory; more specifically, spectral approximation, the approximate solution of integral and operator equations, regularization of inverse and ill-posed problems. He has authored three books, Functional Analysis: A First Course (PHI-Learning, New Delhi), Linear Operator Equations: Approximation and Regularization (World Scientific, Singapore), Calculus of One Variable (Ane Books, New Delhi), and co-authored a book, Linear Algebra (Springer). He published over 75 research papers in nationally and internationally reputed journals, including the Journal of Indian Mathematical Society, Proceedings of Indian Academy of Sciences, Proceedings of the American Mathematical Society, Journal of Integral Equations and Operator Theory, Mathematics of Computation, Numerical Functional Analysis and Optimization, Journal of Inverse and Ill-Posed Problems, and Inverse Problems. He received many awards for his academic achievements, including the C.L. Chandna award of the Indo-Canadian Math Foundation for outstanding contributions in mathematics research and teaching for the year 2003, and Ganesh Prasad Memorial Award of the Indian Mathematical Society for the year 2015. He is a life member of academic bodies such as the Indian Mathematical Society and Ramanujan Mathematical Society.
Summary
The concepts from the theory of measure and integration are vital to any advanced course in analysis specifically in the applications of functional analysis to other areas such as harmonic analysis, partial differential equations, and integral equations. The book is meant for a one-semester course for the graduates of mathematics.
