Introduction to Hilbert Spaces with Applications

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9780122084355: Introduction to Hilbert Spaces with Applications

This book provides the reader with a systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis with diverse applications to differential and integral equations. The Hilbert space formalism is used to develop the foundation of quantum mechanics and the Hilbert space methods are applied to optimization, variational, and control problems and to problems in approximation theory, nonlinear instablity, and bifurcation. Another attractive feature is a simple introduction to the Lebesgue integral. It is intended for senior undergraduate and graduate courses in Hilbert space and functional analysis with applications for students in mathematics, physics, and engineering.

n Systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis
n Great variety of applications that are not available in comparable books
n Different approach to the Lebesgue integral, which makes the theory easier, more intuitive, and more accessible to undergraduate students

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Book Description:

Updated edition presents readers with the basic ideas and results of Hilbert space theory and functional analysis

From the Back Cover:

The Second Edition if this successful text offers a systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis. It includes a simple introduction to the Lebesgue integral and a new chapter on wavelets. The book provides the reader with revised examples and updated diverse applications to differential and integral equations with clear explanations of these methods as applied to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation.
Key Features and Enhancements in the New Edition
* Systematic exposition of the basic ideas and results of Hilbert space theory
* Introduction to the Lebesgue integral
* New chapter on wavelets
* Improved presentation on results and proof
* Revised examples and updated applications
* Completely updated list of references

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Debnath, Lokenath; Mikusinski, Piotr
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