Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Canonical divisors in weighted Bergman spaces


Author: Rachel J. Weir
Journal: Proc. Amer. Math. Soc. 130 (2002), 707-713
MSC (2000): Primary 32A36; Secondary 33C05
DOI: https://doi.org/10.1090/S0002-9939-01-06214-1
Published electronically: June 20, 2001
MathSciNet review: 1866024
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Canonical divisors in Bergman spaces can be found as solutions of extremal problems. We derive a formula for certain extremal functions in the weighted Bergman spaces $A^p_{\alpha}$ for $\alpha > -1$ and $1 \leq p < \infty$. This leads to a study of the zeros of a specific family of hypergeometric functions.


References [Enhancements On Off] (What's this?)

  • 1. P. Duren, D. Khavinson, H.S. Shapiro and C. Sundberg, Contractive zero-divisors in Bergman spaces, Pacific J. Math. 157 (1993), 37-56. MR 94c:30048
  • 2. H. Hedenmalm, A factorization theorem for square area-integrable analytic functions, J. Reine Angew. Math. 422 (1991), 45-68. MR 93c:30053
  • 3. H. Hedenmalm and K. Zhu, On the failure of optimal factorization for certain weighted Bergman spaces, Complex Variables Theory Appl. 19 (1992), 165-176. MR 95f:30064
  • 4. K.Y. Osipenko and M.I. Stessin, On optimal recovery of a holomorphic function in the unit ball of $\mathbb{C} ^n$, Constr. Approx. 8 (1992), 141-159. MR 93d:32008
  • 5. E.D. Rainville, Special Functions, Macmillan, New York, 1960. MR 21:6447
  • 6. S.M. Shimorin, Factorization of analytic functions in weighted Bergman spaces, Algebra i Analiz 5 (1993), no. 5, 155-177 (Russian); St. Petersburg Math. J. 5 (1994), 1005-1022. MR 95j:30032
  • 7. -, On a family of conformally invariant operators, Algebra i Analiz 7 (1995), no. 2, 133-158 (Russian); St. Petersburg Math. J. 7 (1996), 287-306. MR 96i:47010

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32A36, 33C05

Retrieve articles in all journals with MSC (2000): 32A36, 33C05


Additional Information

Rachel J. Weir
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Address at time of publication: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email: rjweir@math.lsa.umich.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06214-1
Received by editor(s): August 22, 2000
Published electronically: June 20, 2001
Additional Notes: The contents of this paper forms a part of the author’s doctoral dissertation at the University of Michigan, written under the direction of Professor Peter Duren, whose support and guidance the author gratefully acknowledges
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society