Pick interpolation and Hilbert function spaces / Jim Agler, John E. McCarthy.
| Author/creator | Agler, Jim |
| Other author | McCarthy, John E. (John Edward), 1964- |
| Format | Book |
| Publication Info | Providence, R.I. : American Mathematical Society, ©2002. |
| Description | xix, 308 pages ; 26 cm. |
| Subjects |
| Series | Graduate studies in mathematics, 1065-7339 ; v. 44 Graduate studies in mathematics ; v. 44. ^A347883 |
| Contents | 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. |
| Bibliography note | Includes bibliographical references (pages 293-301) and index. |
| LCCN | 2001056501 |
| ISBN | 0821828983 (alk. paper) |
| ISBN | 9780821828984 (alk. paper) |