Graduate Studies in Mathematics 2002; 308 pp; hardcover Volume: 44 ISBN10: 0821828983 ISBN13: 9780821828984 List Price: US$57 Member Price: US$45.60 Order Code: GSM/44
 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. Readership Graduate students and research mathematicians interested in operator theory, function spaces, and analysis. Reviews "Written in a clear, straightforward style, at a level to make it accessible to someonea midlevel graduate student, saywho 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 Table of Contents  Prerequisites and notation
 Introduction
 Kernels and function spaces
 Hardy spaces
 \(P^2(\mu)\)
 Pick redux
 Qualitative properties of the solution of the Pick problem in \(H^\infty(\mathbb{D})\)
 Characterizing kernels with the complete Pick property
 The universal Pick kernel
 Interpolating sequences
 Model theory I: Isometries
 The bidisk
 The extremal three point problem on \(\mathbb{D}^2\)
 Collections of kernels
 Model theory II: Function spaces
 Localization
 Schur products
 Parrott's lemma
 Riesz interpolation
 The spectral theorem for normal \(m\)tuples
 Bibliography
 Index
