Introduction to Hilbert Spaces with Applications

This book provides the reader with a systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis with diverse applications to differential and integral equations. The Hilbert space formalism is used to develop the foundation of quantum mechanics and the Hilbert space methods are applied to optimization, variational, and control problems and to problems in approximation theory, nonlinear instablity, and bifurcation. Another attractive feature is a simple introduction to the Lebesgue integral. It is intended for senior undergraduate and graduate courses in Hilbert space and functional analysis with applications for students in mathematics, physics, and engineering.

n Systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis
n Great variety of applications that are not available in comparable books
n Different approach to the Lebesgue integral, which makes the theory easier, more intuitive, and more accessible to undergraduate students

Lokenath Debnath is Professor of the Department of Mathematics and Professor of Mechanical and Aerospace Engineering at the University of Central Florida in Orlando. He received his M.Sc. and Ph.D. degrees in pure mathematics from the University of Calcutta, and obtained D.I.C. and Ph.D. degrees in applied mathematics from the Imperial College of Science and Technology, University of London. He was a Senior Research Fellow at the University of Cambridge and has had visiting appointments to several universities in the United States and abroad. His many honors and awards include two Senior Fulbright Fellowships and an NSF Scientist award to visit India for lectures and research. Dr. Debnath is author or co-author of several books and research papers in pure and applied mathematics, and serves on several editorial boards for scientific journals. He is the current and founding Managing Editor of the International Journal of Mathematics and Mathematical Sciences.

Piotr Mikusinski received his Ph.D. in mathematics from the Institute of Mathematics of the Polish Academy of Sciences. In 1983, he became visiting lecturer at the University of California at Santa Barbara, where he spent two years. He is currently a member of the faculty in the Department of Mathematics at the University of Central Florida in Orlando. His main research interests are the theory of generalized functions and real analysis. He has published many research articles and is co-author with his father, Jan Mikusinski, of An Introduction to Analysis: From Number to Integral.