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Pick Interpolation and Hilbert Function Spaces

About this Title

Jim Agler, University of California at San Diego, San Diego, CA and John E. McCarthy, Washington University, St. Louis, MO

Publication: Graduate Studies in Mathematics
Publication Year: 2002; Volume 44
ISBNs: 978-0-8218-2898-4 (print); 978-1-4704-2095-6 (online)
DOI: https://doi.org/10.1090/gsm/044
MathSciNet review: MR1882259
MSC: Primary 47-02; Secondary 30D55, 30E05, 30H05, 32A70, 46E22, 47A20, 47A57

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Table of Contents

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Front/Back Matter

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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