Pick Interpolation and Hilbert Function Spaces
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A01=Jim Agler
A01=John E. McCarthy
Author_Jim Agler
Author_John E. McCarthy
Category=PBK
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Product details
- ISBN 9781470468552
- Publication Date: 01 Jan 2002
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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.
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.
Jim Agler, University of California at San Diego, CA.
John E. McCarthy, Washington University, St. Louis, MO.
John E. McCarthy, Washington University, St. Louis, MO.
