Introduction To Hilbert Spaces With Applications / Edition 3

by Lokenath Debnath, Piotr Mikusinski

Overview

Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, 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

Product Details

ISBN-13:	9780122084386
Publisher:	Elsevier Science
Publication date:	09/29/2005
Edition description:	REV
Pages:	600
Product dimensions:	1.50(w) x 9.00(h) x 6.00(d)

About the Author

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.

Table of Contents

CHAPTER 1 Normed Vector Spaces
CHAPTER 2 The Lebesgue Integral
CHAPTER 3 Hilbert Spaces and Orthonormal Systems
CHAPTER 4 Linear Operators on Hilbert Spaces
CHAPTER 5 Applications to Integral and Differential Equations
CHAPTER 6 Generalized Functions and Partial Differential Equations
CHAPTER 7 Mathematical Foundations of Quantum Mechanics
CHAPTER 8 Wavelets and Wavelet Transforms
CHAPTER 9 Optimization Problems and Other Miscellaneous Applications

Editorial Reviews

"I think this is a superb text for an applied math class (at the upper level undergraduate or graduate level)! The introduction to Hilbert spaces and other material presented in Chapters 1–4 open the doors to a number of applications as presented in Chapters 5–9.", Robert Gardner, East Tennessee State University.

"This is a unique book which includes both a rigorous development of issues related to Hilbert Spaces, but also gives a wide variety of useful applications..." Joseph M. Powers, University of Notre Dame

From the Publisher

This attractively conceived and executed text for graduate and advanced undergraduate students derives from class notes developed at Georgia Tech and at the U. of Central Florida (Orlando). Part I (four chapters) treats the theoretical essentials. Part II provides review of applications to integral/differential equations, to generalized functions and partial differential equations, to quantum mechanics, to optimization problems and related topics. The text is punctuated at frequent intervals by examples, there are exercises (with hints and selected solutions) at the end of each of the eight chapters, and the bibliography conforms well to the spirit of the text. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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