Hilbert Spaces with Applications

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Academic Press, 2005 - Mathematics - 580 pages
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Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, 3E, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory.

* Updated chapter on wavelets
* Improved presentation on results and proof
* Revised examples and updated applications
* Completely updated list of references .
 

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Contents

Normed Vector Spaces
1
The Lebesgue Integral
39
Hilbert Spaces and Orthonormal Systems
93
Linear Operators on Hilbert Spaces
145
Applications to Integral and Differential Equations
217
Generalized Functions and Partial Differential Equations
287
Mathematical Foundations of Quantum Mechanics
351
Wavelets and Wavelet Transforms
433
Optimization Problems and Other Miscellaneous Applications
477
Hints and Answers to Selected Exercises
547
Bibliography
565
Index
571
Copyright

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About the author (2005)

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.

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