Hardcover ISBN:  9780821891711 
Product Code:  GSM/156 
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eBook ISBN:  9781470418588 
Product Code:  GSM/156.E 
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AMS Member Price:  $68.00 
Hardcover ISBN:  9780821891711 
eBook: ISBN:  9781470418588 
Product Code:  GSM/156.B 
List Price:  $220.00 $177.50 
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AMS Member Price:  $176.00 $142.00 
Hardcover ISBN:  9780821891711 
Product Code:  GSM/156 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470418588 
Product Code:  GSM/156.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821891711 
eBook ISBN:  9781470418588 
Product Code:  GSM/156.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 

Book DetailsGraduate Studies in MathematicsVolume: 156; 2014; 372 ppMSC: Primary 46; 35
This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact selfadjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn–Banach theorem provide a steppingstone to more advanced texts.
The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailormade in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level.
ReadershipGraduate students interested in functional analysis and its applications, e.g., to differential equations and Fourier analysis.

Table of Contents

Chapters

Chapter 1. Inner product spaces

Chapter 2. Normed spaces

Chapter 3. Distance and approximation

Chapter 4. Continuity and compactness

Chapter 5. Banach spaces

Chapter 6. The contraction principle

Chapter 7. The Lebesgue spaces

Chapter 8. Hilbert space fundamentals

Chapter 9. Approximation theory and Fourier analysis

Chapter 10. Sobolev spaces and the Poisson problem

Chapter 11. Operator theory I

Chapter 12. Operator theory II

Chapter 13. Spectral theory of compact selfadjoint operators

Chapter 14. Applications of the spectral theorem

Chapter 15. Baire’s theorem and its consequences

Chapter 16. Duality and the HahnBanach theorem

Historical remarks

Appendix A. Background

Appendix B. The completion of a metric space

Appendix C. Bernstein’s proof of Weierstrass’ theorem

Appendix D. Smooth cutoff functions

Appendix E. Some topics from Fourier analysis

Appendix F. General orthonormal systems


Additional Material

Reviews

Markus Haase's beautiful book lives up to its promise: it provides a wellstructured and gentle introduction to the fundamental concepts of functional analysis. The presentation is clear, the applications are insightful, and the large collection of exercises allow us to deepen the study of the presented material. Graduate students, as well as interested undergraduate students, can easily profit from this wellwritten book.
Béla Gábor Pusztai, ACTA Sci. Math.


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This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact selfadjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn–Banach theorem provide a steppingstone to more advanced texts.
The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailormade in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level.
Graduate students interested in functional analysis and its applications, e.g., to differential equations and Fourier analysis.

Chapters

Chapter 1. Inner product spaces

Chapter 2. Normed spaces

Chapter 3. Distance and approximation

Chapter 4. Continuity and compactness

Chapter 5. Banach spaces

Chapter 6. The contraction principle

Chapter 7. The Lebesgue spaces

Chapter 8. Hilbert space fundamentals

Chapter 9. Approximation theory and Fourier analysis

Chapter 10. Sobolev spaces and the Poisson problem

Chapter 11. Operator theory I

Chapter 12. Operator theory II

Chapter 13. Spectral theory of compact selfadjoint operators

Chapter 14. Applications of the spectral theorem

Chapter 15. Baire’s theorem and its consequences

Chapter 16. Duality and the HahnBanach theorem

Historical remarks

Appendix A. Background

Appendix B. The completion of a metric space

Appendix C. Bernstein’s proof of Weierstrass’ theorem

Appendix D. Smooth cutoff functions

Appendix E. Some topics from Fourier analysis

Appendix F. General orthonormal systems

Markus Haase's beautiful book lives up to its promise: it provides a wellstructured and gentle introduction to the fundamental concepts of functional analysis. The presentation is clear, the applications are insightful, and the large collection of exercises allow us to deepen the study of the presented material. Graduate students, as well as interested undergraduate students, can easily profit from this wellwritten book.
Béla Gábor Pusztai, ACTA Sci. Math.