000			02962nam a22003257a 4500
005			20220531120903.0
008			220325b |||||||| |||| 00| 0 eng d
020			_a9780821828984
028			_a;Zafaa Books & Distributors _b:313/56F 49A, Anand Nagar Inderlok Delhi 110035 _c:ZBD0848 _d:19/03/2022
082			_a515.733 AGL
100			_aAgler, Jim Agler, Jim;
245			_aPick interpolation and Hilbert function Spaces _c/ Jim Agler;
260			_aProvidence, R.I. island _b: American Mathematical Society, _c©2002.
300			_axix, 308 pages _c 26 cm
365			_b10840
490			_aGraduate studies in mathematics, v. 44.
505			_a 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.
520			_aPresents 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
650			_aMathematics
650			_aAnalysis
650			_aHilbert space.
650			_aInterpolation.
650			_aFunctions of complex variables.
650			_aEspace de Hilbert.
650			_aFonctions d'une variable complexe.
650			_aInterpolation
700			_a Agler, Jim;
700			_aMcCarthy, John E.
942			_cBOOK
999			_c58965 _d58965