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Regular sets of sampling and interpolation for weighted Bergman spaces


Author: Kristian Seip
Journal: Proc. Amer. Math. Soc. 117 (1993), 213-220
MSC: Primary 30D50; Secondary 30E10, 46E20
MathSciNet review: 1111222
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Abstract: Let $ {z_{mn}} = {a^m}(bn + i),\;a > 1,\;b > 0,\;m,\;n$ integers. For each weighted Bergman space on the upper half-plane there exists a constant $ c > 0$ such that $ \{ {z_{mn}}\} $ is a set of sampling if and only if $ b\,\ln \,a < c$ and a set of interpolation if and only if $ b\,\ln \,a > c$. When $ b\,\ln \,a = c$, $ \{ {z_{mn}}\} $ is a set of uniqueness.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1111222-5
Article copyright: © Copyright 1993 American Mathematical Society