# Pick Interpolation and Hilbert Function Spaces

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
 Bibliography 293 Index 303 BackCover 309 Derechos de autor