Pick Interpolation and Hilbert Function Spaces

Portada
American Mathematical Soc., 2002 - 308 páginas
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.
 

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Contenido

Chapter 0 Prerequisites and Notation
1
Chapter 1 Introduction
7
Chapter 2 Kernels and Function Spaces
15
Chapter 3 Hardy Spaces
35
Chapter 4 Psup2μ
49
Chapter 5 Pick Redux
55
Chapter 6 Qualitative Properties of the Solution of the Pick Problem in HsupD
71
Chapter 7 Characterizing Kernels with the Complete Pick Property
79
Chapter 12 The Extremal Three Point Problem on Dsup2
195
Chapter 13 Collections of Kernels
211
Function Spaces
237
Chapter 15 Localization
263
Appendix A Schur Products
273
Appendix B Parrotts Lemma
277
Appendix C Riesz Interpolation
281
Appendix D The Spectral Theorem for Normal mTuples
287

Chapter 8 The Universal Pick Kernel
97
Chapter 9 Interpolating Sequences
125
Isometries
151
Chapter 11 The Bidisk
167

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