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Cover Art
PRINTED BOOKS
Author Duren, Peter L., 1935-

Title Bergman spaces / Peter Duren, Alexander Schuster.

Published Providence, RI : American Mathematical Society, 2004.

Copies

Location Call No. Status
 UniM ERC  515.73 DURE    AVAILABLE
Physical description x, 318 pages ; 26 cm.
Series Mathematical surveys and monographs, 0076-5376 ; v. 100.
Mathematical surveys and monographs ; no. 100.
Bibliography Includes bibliographical references and index.
Contents Chapter 1. Bergman Kernel Function 7 -- 1.1. Point-evaluation functionals 7 -- 1.2. Orthonormal bases 9 -- 1.3. Conformal invariance 12 -- 1.4. An extremal problem 14 -- 1.5. Connection with Green's function 16 -- 1.6. Biharmonic Green function 18 -- Chapter 2. Linear Space Properties 25 -- 2.1. Hardy spaces 25 -- 2.2. Strict and uniform convexity 28 -- 2.3. Bergman projection 30 -- 2.4. Dual spaces 35 -- 2.5. Pseudohyperbolic metric 38 -- 2.6. Bloch space 43 -- 2.7. Harmonic conjugates 54 -- 2.8. Linear isometries 56 -- 2.9. Function multipliers 59 -- 2.10. Carleson measures 61 -- 2.11. Uniformly discrete sequences 67 -- Chapter 3. Analytic Properties 73 -- 3.1. More on Hardy spaces 73 -- 3.2. Growth of functions in Bergman spaces 77 -- 3.3. Coefficients of functions in Bergman spaces 81 -- 3.4. Coefficient multipliers 86 -- 3.5. Korenblum's maximum principle 90 -- Chapter 4. Zero-Sets 93 -- 4.2. Density of zero-sets 96 -- 4.3. Dependence on p 98 -- 4.4. Unions and subsets of zero-sets 101 -- 4.5. Blaschke products as generators 106 -- 4.6. Universal divisors 107 -- 4.7. Perturbations of zero-sets 114 -- 4.8. Zeros on a radial line 116 -- Chapter 5. Contractive Zero-Divisors 119 -- 5.1. An extremal problem 119 -- 5.2. Expansive multipliers 127 -- 5.3. Proof of the integral formula 131 -- 5.4. Representation by kernel functions 137 -- 5.5. Analytic continuation 141 -- 5.6. Contractive divisors 144 -- 5.7. Invariant subspaces 146 -- Chapter 6. Sampling and Interpolation 153 -- 6.1. Definitions and motivations 153 -- 6.2. Interpolation in Hardy spaces 157 -- 6.3. A family of sampling and interpolation sequences 159 -- 6.4. Some explicit examples 168 -- 6.5. Density theorems 171 -- 6.6. Direct calculation of densities 176 -- 6.7. Sharpened forms of Horowitz' theorems 182 -- 6.8. Sufficient conditions with the pseudohyperbolic metric 187 -- 6.9. Duality relations 192 -- Chapter 7. Proofs of Sampling and Interpolation Theorems 197 -- 7.1. Perturbation of sampling sequences 197 -- 7.2. Necessity of the sampling condition 204 -- 7.3. Sampling in the growth space 207 -- 7.4. Sufficiency of the sampling condition in A[superscript p] 216 -- 7.5. Sufficiency of the interpolation condition 219 -- 7.6. Necessity of the interpolation condition 234 -- 7.7. Weak interpolation 240 -- Chapter 8. Invariant Subspaces 245 -- 8.1. Beurling's theory for Hardy spaces 245 -- 8.2. Cyclic inner functions in Bergman spaces 247 -- 8.3. Cyclic elements of Bergman spaces 258 -- 8.4. Index of an invariant subspace 261 -- 8.5. Invariant subspaces of higher index 263 -- 8.6. Generalizations to A[superscript p] 265 -- Chapter 9. Structure of Invariant Subspaces 271 -- 9.1. Description of generators 271 -- 9.2. Inner and outer functions for Bergman spaces 273 -- 9.3. Generalization of the main theorem 276 -- 9.4. Cyclic subspaces of A[superscript p] 282 -- 9.5. Extremal functions as generators 288.
Other author Schuster, Alexander, 1968-
Subject Bergman spaces.
ISBN 0821808109 (alk. paper)