Pick interpolation and Hilbert function spaces / Jim Agler, John E. McCarthy.

Format:

Book

Author/Creator:

Agler, Jim, author.

McCarthy, John E. (John Edward), 1964- author.

Series:

Graduate studies in mathematics ; v. 44.

Graduate studies in mathematics, 1065-7339 ; volume 44

Language:

English

Subjects (All):

Hilbert space.

Interpolation.

Functions of complex variables.

Physical Description:

1 online resource (330 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2002]

Language Note:

English

Summary:

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.

Contents:

""Â6.3. Another formula for the solution""""Â6.4. The Nevanlinna problem""; ""Chapter 7. Characterizing Kernels with the Complete Pick Property""; ""Â7.1. Characterization of the complete Pick property""; ""Â7.2. Another characterization of the complete Pick property""; ""Â7.3. Holomorphic spaces with the complete Pick property""; ""Â7.4. The Sobolev space""; ""Â7.5. The M[sub(sxt)] Pick property""; ""Â7.6. Historical notes""; ""Chapter 8. The Universal Pick Kernel""; ""Â8.1. The universal kernel""; ""Â8.2. The realization formula for the universal kernel""

""Â9.5. Grammians bounded above and below""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 293-301) and index.

Description based on print version record.

ISBN:

1-4704-2095-3