Growth of entire harmonic functions in \(\mathbb{R}^n, n\geq 2\), having index pair \((p,q)\) (Q2747440)
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scientific article; zbMATH DE number 1657762
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Growth of entire harmonic functions in \(\mathbb{R}^n, n\geq 2\), having index pair \((p,q)\) |
scientific article; zbMATH DE number 1657762 |
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8 May 2002
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harmonic functions
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entire functions
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slow growth
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fast growth
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Growth of entire harmonic functions in \(\mathbb{R}^n, n\geq 2\), having index pair \((p,q)\) (English)
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In order to classify entire functions of slow growth or fast growth, \textit{O. P. Juneja, G. P. Kapoor} and \textit{S. K. Bajpai} [J. Reine Angew. Math. 282, 53-67 (1976; Zbl 0321.30031); ibid. 290, 180-190 (1977; Zbl 0501.30021)] introduced the notions of \((p,q)\)-order and \((p,q)\)-type. In the paper under review, these notions are extended to harmonic functions on \(\mathbb{R}^n\). Expressions are obtained for the \((p,q)\)-order and \((p,q)\)-type of any non-constant harmonic function \(h\) on \(\mathbb{R}^n\), in terms of the norm of the \(m\)-th gradient of \(h\) at the origin.
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