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
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