Pick Interpolation and Hilbert Function Spaces(Graduate Studies in Mathematics)

选取插值和希尔伯特函数空间

数学分析

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作      者
出版时间
2022年12月30日
装      帧
平装
ISBN
9781470468552
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页      码
308
语      种
英文
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图书简介
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.
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