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

Jim Agler (author)|John E. McCarthy (author)

Softcover

ISBN 10: 1470468557 ISBN 13: 9781470468552

Publisher: American Mathematical Society, 2002

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.

About this title

About the Author

Jim Agler, University of California at San Diego, CA.

John E. McCarthy, Washington University, St. Louis, MO.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2002
• Language: English
• ISBN 10: 1470468557
• ISBN 13: 9781470468552
• Binding: Paperback
• Number of pages: 308