Pick Interpolation and Hilbert Function Spaces (Paperback)

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.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Graduate Studies in Mathematics
Release date:	December 2022
Authors:	Jim Agler • John E. McCarthy
Format:	Paperback
Pages:	308
ISBN-13:	978-1-4704-6855-2
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis Promotions
LSN:	1-4704-6855-7
Barcode:	9781470468552

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