Theory of Bergman spaces /

Hedenmalm, Haakan.

Theory of Bergman spaces / Hakan Hedenmalm, Boris Korenblum, Kehe Zhu. - New York : Springer, c2000. - ix, 286 p. : ill. ; 25 cm. - Graduate texts in mathematics ; 199 .

Includes bibliographical references (p. [274]-[281]) and index.

The Bergman Spaces
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu
Pages 1-27
The Berezin Transform
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu
Pages 28-51
A p -Inner Functions
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu
Pages 52-97
Zero Sets
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu
Pages 98-135
Interpolation and Sampling
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu
Pages 136-175
Invariant Subspaces
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu
Pages 176-189
Cyclicity
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu
Pages 190-215
Invertible Noncyclic Functions
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu
Pages 216-241
Logarithmically Subharmonic Weights
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu
Pages 242-273
Back Matter

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.

0387987916 (alk. paper) 9780387987910

99053568


Bergman kernel functions.

QA331 / .H36 2000

515 / HED