On the Growth of Infinite-Order Subharmonic Functions in ℂ
For infinite-order functions u subharmonic in \(\mathbb{C}\) with given restrictions on the Riesz masses of a disk of radius r ∈ (0, +∞), we find majorants for the functions \(B\left( {r,u} \right) = \max \left\{ {\left| {u\left( z \right)} \right|:\left| z \right| \leqslant r} \right\}\) an...
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| Date: | 2002 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4165 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | For infinite-order functions u subharmonic in \(\mathbb{C}\) with given restrictions on the Riesz masses of a disk of radius r ∈ (0, +∞), we find majorants for the functions \(B\left( {r,u} \right) = \max \left\{ {\left| {u\left( z \right)} \right|:\left| z \right| \leqslant r} \right\}\) and \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{B} \left( {r,u} \right) = \sup \left\{ {\left| {\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{u} \left( z \right)} \right|:\left| z \right| \leqslant r} \right\}\) , where \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{u}\) is a function conjugate to u. |
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