Regular sets of sampling and interpolation for weighted Bergman spaces

Seip, Kristian

doi:10.1090/S0002-9939-1993-1111222-5

Regular sets of sampling and interpolation for weighted Bergman spaces
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by Kristian Seip

Proc. Amer. Math. Soc. 117 (1993), 213-220

DOI: https://doi.org/10.1090/S0002-9939-1993-1111222-5

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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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