A mean value property for polycaloric functions (Q2815575)
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scientific article; zbMATH DE number 6599587
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A mean value property for polycaloric functions |
scientific article; zbMATH DE number 6599587 |
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29 June 2016
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Pizzetti's formula
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powers of heat operators
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one space dimension
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0.93877864
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0.93541336
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0.93164724
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0.9311823
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0.90778524
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0.8985959
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0.8936459
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A mean value property for polycaloric functions (English)
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Pizzetti formula gives an expression of the mean value of a function \(u(x)\) in a ball, in terms of the powers of the Laplacian \(\Delta^m u(0)\), see \textit{G. Łysik} [Acta Math. Hung. 133, No. 1--2, 133--139 (2011; Zbl 1249.31006)] for a simple proof. Similar formula is valid for the mean value in a parabolic ball, in terms of powers of heat operators, see \textit{F. Da Lio} and \textit{L. Rodino} [Arch. Math. 87, No. 3, 261--271 (2006; Zbl 1101.35007)].NEWLINENEWLINE In the present paper the author gives a simple and elegant study of the parabolic case in one space dimension, recapturing the result of Da Lio and Rodino [loc. cit.]. A related formula for polycaloric functions is deduced.
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