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Book Review
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Book Information
Author(s):
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,
$79.00,
0-8218-0810-9
References:
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- [ARS]
- Aleman, A., Richter, S., Sundberg, C., Beurling's theorem for the Bergman space. Acta Math. 177 (1996), no. 2, 275-310. MR 1440934 (98a:46034)
- [AAG]
- Ali, S., Antoine, J-P., Gazeau, J-P., Coherent states, wavelets and their generalizations. Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 2000. MR 1735075 (2002m:81092)
- [ABFP]
- Apostol, C., Bercovici, H., Foias, C., Pearcy, C., On the theory of the class
 with applications to invariant subspaces and the Bergman shift operator. Advances in invariant subspaces and other results of operator theory (Timisoara and Herculane, 1984), 43-49, Oper. Theory Adv. Appl., 17, Birkhäuser, Basel, 1986. MR 0901058 (88k:47005) - [B]
- Beurling, A., On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948). MR 0027954 (10:381e)
- [Bo]
- Böe, B., Interpolating sequences for Besov spaces. J. Funct. Anal. 192 (2002), no. 2, 319-341. MR 1923404 (2003h:46044)
- [C]
- Carleson, L., An interpolation problem for bounded analytic functions. Amer. J. Math. 80 (1958), 921-930. MR 0117349 (22:8129)
- [CW]
- Coifman, R., Weiss, G. Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 83 (1977), no. 4, 569-645. MR 0447954 (56:6264)
- [DS]
- Duren, P., Schuster, A., Bergman spaces. Mathematical Surveys and Monographs, 100. American Mathematical Society, Providence, RI, 2004. MR 2033762
- [He]
- Hedenmalm, H., A factorization theorem for square area-integrable analytic functions. J. Reine Angew. Math. 422 (1991), 45-68. MR 1133317 (93c:30053)
- [HKZ]
- Hedenmalm, H., Korenblum, B., Zhu, K., Theory of Bergman spaces. Graduate Texts in Mathematics, 199. Springer-Verlag, New York, 2000. MR 1758653 (2001c:46043)
- [Ho]
- Horowitz, C., Zeros of functions in the Bergman spaces. Duke Math. J. 41 (1974), 693-710. MR 0357747 (50:10215)
- [K1]
- Korenblum, B., An extension of the Nevanlinna theory. Acta Math. 135 (1975), no. 3-4, 187-219. MR 0425124 (54:13081)
- [K2]
- -, A Beurling-type theorem. Acta Math. 138 (1976), no. 3-4, 265-293. MR 0447584 (56:5894)
- [R]
- Rochberg, R., Interpolation by functions in Bergman spaces. Michigan Math. J. 29 (1982), no. 2, 229-236. MR 0654483 (83e:30039)
- [S1]
- Seip, K., Beurling type density theorems in the unit disk. Invent. Math. 113 (1993), no. 1, 21-39. MR 1223222 (94g:30033)
- [S2]
- Seip, K., Interpolation and sampling in spaces of analytic functions. University Lecture Series, 33. American Mathematical Society, Providence, RI, 2004. MR 2040080
- [SS]
- Shapiro, H. S., Shields, A. L., On some interpolation problems for analytic functions. Amer. J. Math. 83 (1961), 513-532. MR 0133446 (24:A3280)
- [St]
- Stein, E., Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. With the assistance of Timothy S. Murphy. Princeton Mathematical Series, 43. Monographs in Harmonic Analysis, III. Princeton University Press, Princeton, NJ, 1993. MR 1232192 (95c:42002)
Additional Information:
Reviewer(s):
Richard
Rochberg
Affiliation:
Washington University in St. Louis
Email:
rr@math.wustl.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
42
(2005),
251-256.
MSC
(2000):
Primary 30H05;
Secondary 30-02, 46E15, 46E20, 47B38
DOI:
10.1090/S0273-0979-05-01046-3
PII:
S 0273-0979(05)01046-3
Posted:
January 12, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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