On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane
We obtain the description of the zeros, singular boundary functions, and modules of angular boundary values of the functions $f \neq 0$ which are analytic in the half-plane $C_{+} = \{ z : \Re z > 0 \}$ and satisfy the condition $$( \forall \varepsilon > 0 ) ( \exists c_1 > 0 )...
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| Date: | 2004 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2004
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3803 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We obtain the description of the zeros, singular boundary functions, and modules of angular boundary
values of the functions $f \neq 0$ which are analytic in the half-plane $C_{+} = \{ z : \Re z > 0 \}$ and satisfy the
condition
$$( \forall \varepsilon > 0 ) ( \exists c_1 > 0 ) (\forall z \in \mathbb{Ñ}_{+} ): | f ( z ) | \leq c_1 \exp ( (\sigma + \varepsilon) | z \eta ( | z | ) ), $$,
where $0 \leq \sigma < +\infty$ is a given number and $\eta$ is a positive function continuously differentiable on
$[0; +\infty$ and such that $t\eta'(t)/\eta(t) \rightarrow 0$ as $t \rightarrow + \infty$/
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