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Pick Interpolation and Hilbert Function Spaces

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Pick Interpolation and Hilbert Function Spaces Synopsis

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.

About This Edition

ISBN: 9781470468552
Publication date:
Author: Jim Agler, John E McCarthy
Publisher: American Mathematical Society
Format: Paperback
Pagination: 308 pages
Series: Graduate Studies in Mathematics
Genres: Calculus and mathematical analysis