Uniform densities of regular sequences in the unit disk

Authors:
Peter L. Duren, Alexander P. Schuster and Kristian Seip

Journal:
Trans. Amer. Math. Soc. **352** (2000), 3971-3980

MSC (2000):
Primary 30H05, 46E15

DOI:
https://doi.org/10.1090/S0002-9947-00-02602-7

Published electronically:
May 22, 2000

MathSciNet review:
1707485

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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.

**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:
https://doi.org/10.1090/S0002-9947-00-02602-7

Received by editor(s):
July 10, 1998

Published electronically:
May 22, 2000

Article copyright:
© Copyright 2000
American Mathematical Society