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 $H^\infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^\infty$ 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 the interpolation 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
Chapter 0 Prerequisites and Notation | 1 |
Chapter 1 Introduction | 7 |
Chapter 2 Kernels and Function Spaces | 15 |
Chapter 3 Hardy Spaces | 35 |
Chapter 4 Psup2μ | 49 |
Chapter 5 Pick Redux | 55 |
Chapter 6 Qualitative Properties of the Solution of the Pick Problem in HsupD | 71 |
Chapter 7 Characterizing Kernels with the Complete Pick Property | 79 |
Chapter 12 The Extremal Three Point Problem on Dsup2 | 195 |
Chapter 13 Collections of Kernels | 211 |
Function Spaces | 237 |
Chapter 15 Localization | 263 |
Appendix A Schur Products | 273 |
Appendix B Parrotts Lemma | 277 |
Appendix C Riesz Interpolation | 281 |
Appendix D The Spectral Theorem for Normal mTuples | 287 |
Chapter 8 The Universal Pick Kernel | 97 |
Chapter 9 Interpolating Sequences | 125 |
Isometries | 151 |
Chapter 11 The Bidisk | 167 |
| 293 | |
| 303 | |
BackCover | 309 |
מהדורות אחרות - הצג הכל
מונחים וביטויים נפוצים
adjoint admissible kernel analytic assume ball of H*(D Banach Bergman space bidisk Blaschke product bounded point evaluations C*-algebra C1 GB C2 GB Carleson measure Chapter cl(D closed unit ball co-isometric extension commutant lifting theorem complete Pick kernel complete Pick property completely positive complex numbers coordinate function Corollary define Definition denote dilation direct sum Dirichlet space disk Exercise exists function f Grammian Hardy space hence Hilbert function space Hilbert space holomorphic functions inequality interpolating interpolating sequence isometry kernel function Lebesgue measure Lemma Let H linear m-tuple Moreover Mult(H multiplier algebra nodes non-zero norm normalized notation orthogonal projection Pick matrix Pick problem Pick's theorem positive semi-definite proof of Theorem prove rational function representation satisfies Schur product self-adjoint solution space H spectral strongly separated subset Suppose Szegó kernel uniform algebra unique unitary vanish vector weak kernels weak-star topology weakly separated zero set