A form of classical Picard principle (Q1917597)
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scientific article; zbMATH DE number 897703
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A form of classical Picard principle |
scientific article; zbMATH DE number 897703 |
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A form of classical Picard principle (English)
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14 August 1997
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The following result is proved. Let \(u\) be harmonic in a deleted neighbourhood of the origin in \(\mathbb{R}^d\). Suppose that \(u(x)\geq o(|x|^{-d+1})\) as \(x\) tends to zero. Then \( u = cH_d +v \) where \(H_d\) is the fundamental (radial) harmonic function and \(v\) is harmonic in a neighbourhood of the origin. The proof uses expansions in spherical harmonics.
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harmonic function
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expansions in spherical harmonics
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