A First Course in Functional Analysis: Theory and Applications

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Anthem Press, Feb 1, 2013 - Mathematics - 486 pages
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This book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.

 

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Contents

Normed Linear Spaces 5890
58
Hilbert Space 91129
91
Linear Operators 130178
130
Linear Functionals 179220
179
Space of Bounded Linear Functionals 221266
221
Closed Graph Theorem and Its Consequences 267281
267
Compact Operators on Normed Linear Spaces 282322
282
Elements of Spectral Theory of SelfAdjoint 323353
323
Unbounded Linear Operators 381399
381
The HahnBanach Theorem and Optimization 400409
400
Variational Problems 410429
410
The Wavelet Analysis 430442
430
Dynamical Systems 443453
443
List of Symbols 454458
454
Index 463468
463
Copyright

Measure and Integration in Lp Spaces 354380
354

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About the author (2013)

Rabindranath Sen is a retired professor and former head of the Department of Applied Mathematics at the University of Calcutta.

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