Haakan Hedenmalm, Boris Korenblum, Kehe Zhu (auth.)9780387987910, 0387987916
Preliminary Text. Do not use. 15 years ago the function theory and operator theory connected with the Hardy spaces was well understood (zeros; factorization; interpolation; invariant subspaces; Toeplitz and Hankel operators, etc.). None of the techniques that led to all the information about Hardy spaces worked on their close relatives the Bergman spaces. Most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely. Now the situation has completely changed. Today there are rich theories describing the Bergman spaces and their operators. Research interest and research activity in the area has been high for several years. A book is badly needed on Bergman spaces and the three authors are the right people to write it. |
Table of contents :
Front Matter….Pages i-ix
The Bergman Spaces….Pages 1-27
The Berezin Transform….Pages 28-51
A p -Inner Functions….Pages 52-97
Zero Sets….Pages 98-135
Interpolation and Sampling….Pages 136-175
Invariant Subspaces….Pages 176-189
Cyclicity….Pages 190-215
Invertible Noncyclic Functions….Pages 216-241
Logarithmically Subharmonic Weights….Pages 242-273
Back Matter….Pages 274-289 |
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