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This article is cited in 4 scientific papers (total in 4 papers)
Research Papers
Lower bounds on the values of an entire function of exponential type at certain integers, in terms of a least superharmonic majorant
P. Koosisa, Henrik L. Pedersenb a Mathematics Department, McGill University, Montreal, Québec, Canada
b Matematisk Afdeling, Københavns Universitet, København, Denmark
Abstract:
In this,paper and the following one, it is shown that if $A<\pi$ and $\eta>0$ is
sufficiently small (depending on $A$), the entire functions $f(z)$ of exponential type $\le A$
satisfying $\sum^{\infty}_{m=-\infty}(\log^+|f(n)|/(1+n^2))\le\eta$ form a normal family (in $\mathbb C$). General properties of least superharmonic majorants are used to obtain this result, and from it
the multiplier theorem of Beurling and Malliavin is readily derived.
Keywords:
Entire function of exponential type, least superharmonic majorant, logarithmic sum, BeurlingT-Malliavin multiplier theorem.
Received: 27.10.1997
Citation:
P. Koosis, Henrik L. Pedersen, “Lower bounds on the values of an entire function of exponential type at certain integers, in terms of a least superharmonic majorant”, Algebra i Analiz, 10:3 (1998), 31–44; St. Petersburg Math. J., 10:3 (1999), 429–439
Linking options:
https://www.mathnet.ru/eng/aa995 https://www.mathnet.ru/eng/aa/v10/i3/p31
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Abstract page: | 376 | Full-text PDF : | 130 | First page: | 1 |
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