An applied understanding of functional analysis is essential for students pursuing research or careers in pure mathematics, applied mathematics, mathematical physics, and engineering, among other disciplines.
Functional Analysis: Theory and Applications offers a comprehensive exploration of functional analysis. Authored by esteemed mathematicians with extensive expertise in the field, this book thoroughly introduces fundamental concepts in functional analysis, including Banach spaces, Hilbert spaces, operator theory, nonlinear analysis, linear operators, and normed spaces, and implements these in real-world problems across various scientific and engineering disciplines.
The book's rigorous mathematical treatment is combined with worked examples, exercises and solutions, visual aids, application case studies, and future directions across all chapters to reinforce learning, while appendices offer supplementary materials, proofs of theorems, and tables of important results, among other resources.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. About the authors - p. xi 7. Preface - p. xiii 8. Acknowledgments - p. xv 9. Chapter 1: Normed spaces - p. 1 10. Chapter 2: Banach spaces - p. 19 11. Chapter 3: Bounded linear operators and functionals - p. 35 12. Chapter 4: Inner product spaces and Hilbert spaces - p. 57 13. Chapter 5: Operators on Hilbert spaces - p. 87 14. Chapter 6: Spectral analysis - p. 107 15. Chapter 7: Convex analysis - p. 123 16. Chapter 8: Functional equations - p. 135 17. Chapter 9: Nonlinear analysis - p. 145 18. Chapter 10: Real world applications - p. 155 19. Index - p. 169
An applied understanding of functional analysis is essential for students pursuing research or careers in pure mathematics, applied mathematics, mathematical physics, and engineering, among other disciplines.
Functional Analysis: Theory and Applications offers a comprehensive exploration of functional analysis. Authored by esteemed mathematicians with extensive expertise in the field, this book thoroughly introduces fundamental concepts in functional analysis, including Banach spaces, Hilbert spaces, operator theory, nonlinear analysis, linear operators, and normed spaces, and implements these in real-world problems across various scientific and engineering disciplines.
The book's rigorous mathematical treatment is combined with worked examples, exercises and solutions, visual aids, application case studies, and future directions across all chapters to reinforce learning, while appendices offer supplementary materials, proofs of theorems, and tables of important results, among other resources.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. About the authors - p. xi 7. Preface - p. xiii 8. Acknowledgments - p. xv 9. Chapter 1: Normed spaces - p. 1 10. Chapter 2: Banach spaces - p. 19 11. Chapter 3: Bounded linear operators and functionals - p. 35 12. Chapter 4: Inner product spaces and Hilbert spaces - p. 57 13. Chapter 5: Operators on Hilbert spaces - p. 87 14. Chapter 6: Spectral analysis - p. 107 15. Chapter 7: Convex analysis - p. 123 16. Chapter 8: Functional equations - p. 135 17. Chapter 9: Nonlinear analysis - p. 145 18. Chapter 10: Real world applications - p. 155 19. Index - p. 169
