| Softcover ISBN: | 978-1-4704-6855-2 |
| Product Code: | GSM/44.S |
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| eBook ISBN: | 978-1-4704-2095-6 |
| Product Code: | GSM/44.E |
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| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-6855-2 |
| eBook: ISBN: | 978-1-4704-2095-6 |
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| List Price: | $174.00 $131.50 |
| MAA Member Price: | $156.60 $118.35 |
| AMS Member Price: | $139.20 $105.20 |
| Softcover ISBN: | 978-1-4704-6855-2 |
| Product Code: | GSM/44.S |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| eBook ISBN: | 978-1-4704-2095-6 |
| Product Code: | GSM/44.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-6855-2 |
| eBook ISBN: | 978-1-4704-2095-6 |
| Product Code: | GSM/44.S.B |
| List Price: | $174.00 $131.50 |
| MAA Member Price: | $156.60 $118.35 |
| AMS Member Price: | $139.20 $105.20 |
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Book DetailsGraduate Studies in MathematicsVolume: 44; 2002; 308 ppMSC: Primary 47; 30; 46; 32
The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest \(H^\infty\) norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider \(H^\infty\) as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces.
The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
ReadershipGraduate students and research mathematicians interested in operator theory, function spaces, and analysis.
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Table of Contents
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Chapters
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Chapter 0. Prerequisites and notation
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Chapter 1. Introduction
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Chapter 2. Kernels and function spaces
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Chapter 3. Hardy spaces
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Chapter 4. $P^2(\mu )$
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Chapter 5. Pick redux
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Chapter 6. Qualitative properties of the solution of the Pick problem in $H^\infty (\mathbb {D})$
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Chapter 7. Characterizing kernels with the complete Pick property
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Chapter 8. The universal Pick kernel
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Chapter 9. Interpolating sequences
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Chapter 10. Model theory I: Isometries
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Chapter 11. The bidisk
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Chapter 12. The extremal three point problem on $\mathbb {D}^2$
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Chapter 13. Collections of kernels
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Chapter 14. Model theory II: Function spaces
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Chapter 15. Localization
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Appendix A. Schur products
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Appendix B. Parrott’s lemma
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Appendix C. Riesz interpolation
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Appendix D. The spectral theorem for normal $m$-tuples
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Reviews
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Written in a clear, straightforward style, at a level to make it accessible to someone—a mid-level graduate student, say—who wishes to study the material in detail for the first time ... contains exercises ... as well as ... open questions. It brings the reader up to the current ‘state of the art’ and so will be a valuable resource for the specialist ... would be an excellent basis for a graduate seminar or topics course.
Mathematical Reviews -
Material is wonderfully presented, and the book serves as a lovely introduction to the subject. It is written by two authorities in the field, and helps grad students get entry into an exciting, modern, and very active research area.
Palle Jorgensen
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
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The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest \(H^\infty\) norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider \(H^\infty\) as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces.
The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
Graduate students and research mathematicians interested in operator theory, function spaces, and analysis.
-
Chapters
-
Chapter 0. Prerequisites and notation
-
Chapter 1. Introduction
-
Chapter 2. Kernels and function spaces
-
Chapter 3. Hardy spaces
-
Chapter 4. $P^2(\mu )$
-
Chapter 5. Pick redux
-
Chapter 6. Qualitative properties of the solution of the Pick problem in $H^\infty (\mathbb {D})$
-
Chapter 7. Characterizing kernels with the complete Pick property
-
Chapter 8. The universal Pick kernel
-
Chapter 9. Interpolating sequences
-
Chapter 10. Model theory I: Isometries
-
Chapter 11. The bidisk
-
Chapter 12. The extremal three point problem on $\mathbb {D}^2$
-
Chapter 13. Collections of kernels
-
Chapter 14. Model theory II: Function spaces
-
Chapter 15. Localization
-
Appendix A. Schur products
-
Appendix B. Parrott’s lemma
-
Appendix C. Riesz interpolation
-
Appendix D. The spectral theorem for normal $m$-tuples
-
Written in a clear, straightforward style, at a level to make it accessible to someone—a mid-level graduate student, say—who wishes to study the material in detail for the first time ... contains exercises ... as well as ... open questions. It brings the reader up to the current ‘state of the art’ and so will be a valuable resource for the specialist ... would be an excellent basis for a graduate seminar or topics course.
Mathematical Reviews -
Material is wonderfully presented, and the book serves as a lovely introduction to the subject. It is written by two authorities in the field, and helps grad students get entry into an exciting, modern, and very active research area.
Palle Jorgensen
