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Sets of sampling and interpolation in Bergman spaces

Author(s): Alexander P. Schuster
Journal: Proc. Amer. Math. Soc. 125 (1997), 1717-1725.
MSC (1991): Primary 30H05, 46E15
MathSciNet review: 1396996
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Abstract: Properties of the unions of sampling and interpolation sets for Bergman spaces are discussed in conjunction with the examples given by Seip (1993). Their relationship to the classical interpolation sequences is explored. In addition, the role played by canonical divisors in the study of these sets is examined and an example of a sampling set is constructed in the disk.

References:

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3.: 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
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Additional Information:

Alexander P. Schuster
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Email: aschust@math.lsa.umich.edu

DOI: 10.1090/S0002-9939-97-03899-9
PII: S 0002-9939(97)03899-9
Keywords: Bergman space, sampling, interpolation, zero set, canonical divisor
Received by editor(s): December 7, 1995
Additional Notes: The content 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 help is greatly appreciated.
Communicated by: Theodore W. Gamelin
Copyright of article: Copyright 1997, American Mathematical Society

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