American Mathematical Society

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF This review is available free of charge.
Book Information:

Authors: Peter Duren and Alex Schuster
Title: Bergman spaces
Additional book information: Mathematical Surveys and Monographs, vol. 100, American Mathematical Society, Providence, RI, 2004, x+318 pp., ISBN 0-8218-0810-9, $79.00$

A. Aleman, S. Richter, and C. Sundberg, Beurling’s theorem for the Bergman space, Acta Math. 177 (1996), no. 2, 275–310. MR 1440934, DOI 10.1007/BF02392623

Syed Twareque Ali, Jean-Pierre Antoine, and Jean-Pierre Gazeau, Coherent states, wavelets and their generalizations, Graduate Texts in Contemporary Physics, Springer-Verlag, New York, 2000. MR 1735075, DOI 10.1007/978-1-4612-1258-4

C. Apostol, H. Bercovici, C. Foias, and C. Pearcy, On the theory of the class $\textbf {A}_{\aleph _0}$ with applications to invariant subspaces and the Bergman shift operator, Advances in invariant subspaces and other results of operator theory (Timişoara and Herculane, 1984) Oper. Theory Adv. Appl., vol. 17, Birkhäuser, Basel, 1986, pp. 43–49. MR 901058

Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 239–255. MR 27954, DOI 10.1007/BF02395019

Bjarte Böe, Interpolating sequences for Besov spaces, J. Funct. Anal. 192 (2002), no. 2, 319–341. MR 1923404, DOI 10.1006/jfan.2002.3905

Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930. MR 117349, DOI 10.2307/2372840

Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. MR 447954, DOI 10.1090/S0002-9904-1977-14325-5

Peter Duren and Alexander Schuster, Bergman spaces, Mathematical Surveys and Monographs, vol. 100, American Mathematical Society, Providence, RI, 2004. MR 2033762, DOI 10.1090/surv/100

Håkan Hedenmalm, A factorization theorem for square area-integrable analytic functions, J. Reine Angew. Math. 422 (1991), 45–68. MR 1133317, DOI 10.1515/crll.1991.422.45

Haakan Hedenmalm, Boris Korenblum, and Kehe Zhu, Theory of Bergman spaces, Graduate Texts in Mathematics, vol. 199, Springer-Verlag, New York, 2000. MR 1758653, DOI 10.1007/978-1-4612-0497-8

Charles Horowitz, Zeros of functions in the Bergman spaces, Duke Math. J. 41 (1974), 693–710. MR 357747

Boris Korenblum, An extension of the Nevanlinna theory, Acta Math. 135 (1975), no. 3-4, 187–219. MR 425124, DOI 10.1007/BF02392019

Boris Korenblum, A Beurling-type theorem, Acta Math. 138 (1976), no. 3-4, 265–293. MR 447584, DOI 10.1007/BF02392318

Richard Rochberg, Interpolation by functions in Bergman spaces, Michigan Math. J. 29 (1982), no. 2, 229–236. MR 654483

Kristian Seip, Beurling type density theorems in the unit disk, Invent. Math. 113 (1993), no. 1, 21–39. MR 1223222, DOI 10.1007/BF01244300

Kristian Seip, Interpolation and sampling in spaces of analytic functions, University Lecture Series, vol. 33, American Mathematical Society, Providence, RI, 2004. MR 2040080, DOI 10.1090/ulect/033

H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513–532. MR 133446, DOI 10.2307/2372892

Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192

Review Information:

Reviewer: Richard Rochberg
Affiliation: Washington University in St. Louis
Email: rr@math.wustl.edu

Journal: Bull. Amer. Math. Soc. 42 (2005), 251-256
Published electronically: January 12, 2005
Review copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.