Introduction to Hilbert Spaces with Applications

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.

"...this is a very useful and good book and it can find a place in the library of anybody interested in functional analysis, particularly Hilbert Spaces and their applications." --MAA REVIEWS

• CHAPTER 1 Normed Vector SpacesCHAPTER 2 The Lebesgue IntegralCHAPTER 3 Hilbert Spaces and Orthonormal SystemsCHAPTER 4 Linear Operators on Hilbert SpacesCHAPTER 5 Applications to Integral and Differential EquationsCHAPTER 6 Generalized Functions and Partial Differential EquationsCHAPTER 7 Mathematical Foundations of Quantum MechanicsCHAPTER 8 Wavelets and Wavelet TransformsCHAPTER 9 Optimization Problems and Other Miscellaneous Applications