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Pick Interpolation and Hilbert Function Spaces.
・ISBN 978-1-4704-6855-2 paper US$ 89.00
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| 著者・編者 | Agler, Jim / McCarthy, John E., |
|---|---|
| シリーズ | Graduate Studies in Mathematics |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2002 |
| ページ数 | 308 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-6842＞ |
解説
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.