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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
MathSciNet review:
1707485
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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
 , J. Anal. Math. 67 (1995), 307-322. MR 97c:30044
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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
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