A mean value theorem for polyanalytic functions (Q2901668)
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scientific article; zbMATH DE number 6062198
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A mean value theorem for polyanalytic functions |
scientific article; zbMATH DE number 6062198 |
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31 July 2012
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polyanalytic functions
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mean value theorem
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weighted ball mean value
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A mean value theorem for polyanalytic functions (English)
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In the present paper a mean value theorem for polyanalytic functions is obtained. This problem is connected with many sections of analysis, the theory of elasticity and mechanics. The author considers \(m\)-analytic functions (\(m\in\mathbb{N}\)) and obtains that the weighted ball mean value for a polyanalytic function is equal to a certain sum of partial derivatives of this function. In particular, this result gives a new characterization of polyanalytic functions.
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