Pick Interpolation and Hilbert Function Spaces

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

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

• Prerequisites and notationIntroductionKernels and function spacesHardy spaces$P^2(\mu)$Pick reduxQualitative properties of the solution of the Pick problem in $H^\infty(\mathbb{D})$Characterizing kernels with the complete Pick propertyThe universal Pick kernelInterpolating sequencesModel theory I: IsometriesThe bidiskThe extremal three point problem on $\mathbb{D}^2$Collections of kernelsModel theory II: Function spacesLocalizationSchur productsParrott's lemmaRiesz interpolationThe spectral theorem for normal $m$-tuplesBibliographyIndex