Pick Interpolation and Hilbert Function SpacesAmerican Mathematical Soc., 2002 - 308 עמודים The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $Hinfty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $Hinfty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider theinterpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem,and the hereditary functional calculus. |
תוכן
Prerequisites and Notation | 1 |
Introduction | 7 |
Kernels and Function Spaces | 15 |
Hardy Spaces | 35 |
P2μ | 49 |
Pick Redux | 55 |
Characterizing Kernels with the Complete Pick Property | 79 |
The Universal Pick Kernel | 97 |
The Bidisk | 167 |
The Extremal Three Point Problem on D2 | 195 |
Collections of Kernels | 211 |
Function Spaces | 237 |
Localization | 263 |
Appendix A Schur Products | 273 |
The Spectral Theorem for Normal mTuples | 287 |
| 303 | |
מהדורות אחרות - הצג הכל
מונחים וביטויים נפוצים
adjoint AN+1 assume Banach Bergman Bergman space bidisk Blaschke product bounded point evaluations C*-algebra Chapter closed unit ball co-isometric extension commutant lifting theorem complete Pick kernel complete Pick property completely positive coordinate function Corollary define Definition denote dilation direct sum Dirichlet space disk equivalent Exercise exists Grammian H₁ Hardy space hence Hilbert function space Hilbert space holomorphic functions interpolating sequence interpolation invariant subspace isometry kernel function Lemma Let H linear m-tuple Math measure Moreover Mult(H multiplier algebra nodes non-zero norm normalized notation operator theory orthogonal projection P²(µ Pick matrix Pick problem Pick's theorem polynomials positive semi-definite proof of Theorem prove rational function representation scalar Pick Schur product solution space H spectral subset Suppose Szegő kernel topology uniform algebra unique unitary vanish vector w₁ weak kernels weak-star weak-star topology zero set