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Agler, Jim Agler, Jim;

Pick interpolation and Hilbert function Spaces / Jim Agler; - Providence, R.I. island : American Mathematical Society, ©2002. - xix, 308 pages 26 cm - Graduate studies in mathematics, v. 44. .

Prerequisites and Notation --
Blaschke products --
Pseudo-hyperbolic metric --
Hilbert spaces --
The weak-star topology on B(H) --
Rank one operators --
Analytic functions of several variables --
The Pick problem --
H[superscript [infinity] as an operator algebra --
The operator theory approach to the Pick problem --
The Pick property --
Model theory --
Collections of kernels --
Kernels and Function Spaces --
Hilbert function spaces --
Kernels --
Multipliers --
Tensor products --
Vector-valued Hilbert function spaces --
Rescaling kernels --
Factoring kernels --
Operator-valued kernels --
Historical notes --
Hardy Spaces --
H[superscript p] spaces --
Fatou's theorem --
H[superscript p] spaces again --
H[superscript [infinity] (D) as a multiplier algebra --
Inner functions --
Historical notes --
P[superscript 2] ([mu]) --
Other spaces with H[superscript [infinity] (D) as the multiplier algebra --
Vector-valued P[superscript 2] ([mu]) spaces --
Pick Redux --
Necessity of positivity of the Pick matrix --
The Szego kernel has the Pick property --
The Caratheodory problem --
Uniqueness of the Szego kernel --
Historical notes --
Qualitative Properties of the Solution of the Pick Problem in H[superscript [infinity] (D) --
A formula for the solution --
The realization formula for H[superscript [infinity] (D) --
Another formula for the solution --
The Nevanlinna problem --
Characterizing Kernels with the Complete Pick Property --
Characterization of the complete Pick property --
Another characterization of the complete Pick property.

Presents the theory of reproducing kernel Hilbert spaces. This work discusses 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. It considers $H^\infty$ as the multiplier algebra of the Hardy space and uses Hilbert space techniques to solve the problem

ISBN: 9780821828984

Publisher. No.: Zafaa Books & Distributors :313/56F 49A, Anand Nagar Inderlok Delhi 110035

Subjects--Topical Terms:
Mathematics
Analysis
Hilbert space.
Interpolation.
Functions of complex variables.
Espace de Hilbert.
Fonctions d'une variable complexe.
Interpolation

Dewey Class. No.: 515.733 AGL