Available in electronic format
Available in print format		 Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Uniform densities of regular sequences in the unit disk

Author(s): Peter L. Duren; Alexander P. Schuster; Kristian Seip
Journal: Trans. Amer. Math. Soc. 352 (2000), 3971-3980.
MSC (2000): Primary 30H05, 46E15
Posted: May 22, 2000
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: The upper and lower uniform densities of some regular sequences are computed. These densities are used to determine sequences of sampling and interpolation for Bergman spaces of the unit disk.

References:

1.
C. Horowitz, Zeros of functions in the Bergman spaces, Duke Math. J. 41 (1974), 693-710. MR 55:681

2.
D. Luecking, Zero sequences for Bergman spaces, Complex Variables Theory Appl. 30 (1996), 345-362. MR 97g:30007

3.
A. Schuster, Sets of sampling and interpolation in Bergman spaces, Proc. Amer. Math. Soc. 125 (1997), 1717-1725. MR 97g:46029

4.
A. Schuster, Sampling and interpolation in Bergman spaces, Ph.D. thesis, University of Michigan (1997).

5.
A. Schuster, On Seip's description of sampling sequences for Bergman spaces, Complex Variables Theory Appl. (to appear).

6.
A. Schuster and K. Seip, A Carleson-type condition for interpolation in Bergman spaces, J. Reine Angew. Math. 497 (1998), 223-233. MR 99f:46034

7.
K. Seip, Regular sets of sampling and interpolation for weighted Bergman spaces, Proc. Amer. Math. Soc. 117 (1993), 213-220. MR 93:30051

8.
K. Seip, Beurling type density theorems in the unit disk, Invent. Math. 113 (1994), 21-39. MR 94g:30033

9.
K. Seip, On Korenblum's density condition for the zero sequences of $A^{-\alpha }$, J. Anal. Math. 67 (1995), 307-322. MR 97c:30044

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 30H05, 46E15

Retrieve articles in all Journals with MSC (2000): 30H05, 46E15

Additional Information:

Peter L. Duren
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Email: duren@math.lsa.umich.edu

Alexander P. Schuster
Affiliation: Department of Mathematics, San Francisco State University, San Francisco, California 94132-4163
Email: schuster@sfsu.edu

Kristian Seip
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, N--7034 Trondheim, Norway
Email: seip@math.ntnu.no

DOI: 10.1090/S0002-9947-00-02602-7
PII: S 0002-9947(00)02602-7
Received by editor(s): July 10, 1998
Posted: May 22, 2000
Copyright of article: Copyright 2000, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google