Functional Analysis and Applications

1. Front Matter

   Pages i-xvii

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2. Banach Contraction Fixed Point Theorem

   • Abul Hasan Siddiqi

   Pages 1-14

3. Banach Spaces

   • Abul Hasan Siddiqi

   Pages 15-69

4. Hilbert Spaces

   • Abul Hasan Siddiqi

   Pages 71-143

5. Fundamental Theorems

   • Abul Hasan Siddiqi

   Pages 145-175

6. Differential and Integral Calculus in Banach Spaces

   • Abul Hasan Siddiqi

   Pages 177-225

7. Optimization Problems

   • Abul Hasan Siddiqi

   Pages 227-247

8. Operator Equations and Variational Methods

   • Abul Hasan Siddiqi

   Pages 249-276

9. Finite Element and Boundary Element Methods

   • Abul Hasan Siddiqi

   Pages 277-309

10. Variational Inequalities and Applications

    • Abul Hasan Siddiqi

    Pages 311-350

11. Spectral Theory with Applications

    • Abul Hasan Siddiqi

    Pages 351-380

12. Frame and Basis Theory in Hilbert Spaces

    • Abul Hasan Siddiqi

    Pages 381-397

13. Wavelet Theory

    • Abul Hasan Siddiqi

    Pages 399-463

14. Wavelet Method for Partial Differential Equations and Image Processing

    • Abul Hasan Siddiqi

    Pages 465-495

15. Wavelet Frames

    • Abul Hasan Siddiqi

    Pages 497-508

16. Gabor Analysis

    • Abul Hasan Siddiqi

    Pages 509-519

17. Correction to: Functional Analysis and Applications

    • Abul Hasan Siddiqi

    Pages C1-C1

18. Back Matter

    Pages 521-562

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This self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses the applications of functional analysis in diverse fields. The book is unique in its scope, and a variety of applications of functional analysis and operator-theoretic methods are devoted to each area of application. Each chapter includes a set of problems, some of which are routine and elementary, and some of which are more advanced.

The book is primarily intended as a textbook for graduate and advanced undergraduate students in applied mathematics and engineering. It offers several attractive features making it ideally suited for courses on functional analysis intended to provide a basic introduction to the subject and the impact of functional analysis on applied and computational mathematics, nonlinear functional analysis and optimization. It introduces emerging topics like wavelets, Gabor system, inverse problems and application to signal and image processing.

• Functional Analysis
• Optimization Theory and Algorithms
• Operator Equations
• Finite Elements Methods
• Boundary Elements Methods
• Variational Inequalities
• Inverse Problems and Regularization
• Frames and Wavelet Theory
• Numerical Methods
• Gabor Analysis
• Image Processing
• partial differential equations

• School of Basic Sciences and Research, Sharda University, Greater Noida, India

  Abul Hasan Siddiqi

ABUL HASAN SIDDIQI is a distinguished scientist and professor emeritus at the School of Basic Sciences and Research at Sharda University, Greater Noida, India. Professor Siddiqi has held several important administrative positions such as Chairman, Department of Mathematics, Dean Faculty of Science, Pro-Vice-Chancellor in one of the Central Universities of India—Aligarh Muslim University. He has been actively associated with International Centre for Theoretical Physics, Trieste, Italy (UNESCO organisation) in different capacities for more than 20 years, was professor of Mathematics at King FahadFahd University of Petroleum and Minerals, Saudi Arabia for 10 years, consultant to Sultan Qaboos University, Oman for 5 terms, Istanbul Aydin University, Turkey for three years and Institute of Micro-electronics, Malaysia for five months. Having been awarded three German Academic Exchange Fellowships to carry out mathematical research in Germany, he has also jointly published more than 100 research papers with his research collaborators, 5 books and edited proceedings of 9 international conferences. He is the founder secretary of the Indian Society of Industrial and Applied Mathematics (ISIAM), which celebrated its Silver Jubilee in January 2016. He is editor-in-chief of the Indian Journal of Industrial and Applied Mathematics, published by the ISIAM, and of the book series Industrial and Applied Mathematics with Springer. Recently he has been elected President of ISIAM which represents India at the Apex forum of Industrial and Applied Mathematics-ICIAM.

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