Introduction to Hilbert Spaces with Applications -

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Résumé :
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....

Biographie:
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....

Sommaire:
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...