Items related to Pick Interpolation and Hilbert Function Spaces (Graduate...

Pick Interpolation and Hilbert Function Spaces (Graduate Studies in Mathematics, 44) - Softcover

Book 188 of 190: Graduate Studies in Mathematics

Jim Agler; John E. McCarthy

 
9781470468552: Pick Interpolation and Hilbert Function Spaces (Graduate Studies in Mathematics, 44)
Softcover
ISBN 10: 1470468557 ISBN 13: 9781470468552
Publisher: American Mathematical Society, 2023

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.

"synopsis" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2023
Language
English
ISBN 10 
1470468557
ISBN 13 
9781470468552
Binding
Paperback
Number of pages
308