TY - BOOK AU - Agler, Jim Agler, Jim; AU - Agler, Jim; AU - McCarthy, John E. TI - Pick interpolation and Hilbert function Spaces T2 - Graduate studies in mathematics, v. 44 SN - 9780821828984 U1 - 515.733 AGL PY - 2002/// CY - Providence, R.I. island PB - : American Mathematical Society, KW - Mathematics KW - Analysis KW - Hilbert space KW - Interpolation KW - Functions of complex variables KW - Espace de Hilbert KW - Fonctions d'une variable complexe N1 - 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 N2 - 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 ER -