02962nam a22003257a 4500 20220531120903.0 220325b |||||||| |||| 00| 0 eng d 9780821828984 ;Zafaa Books & Distributors :313/56F 49A, Anand Nagar Inderlok Delhi 110035 :ZBD0848 :19/03/2022 515.733 AGL 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 10840 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 Mathematics Analysis Hilbert space. Interpolation. Functions of complex variables. Espace de Hilbert. Fonctions d'une variable complexe. Interpolation Agler, Jim; McCarthy, John E. BOOK 58965 58965 0 0 ddc 0 0 SNUL SNUL 2022-03-25 Zafaa Books & Distributors 10840.00 1 515.733 AGL 28554 2022-10-16 2022-09-15 00:00:00 2022-09-15 2022-03-25 BOOK Books Shifted to Mathematics Dept (Grant Matrix)