A characterization of convolution and related operations (Q1059234)
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scientific article; zbMATH DE number 3903221
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of convolution and related operations |
scientific article; zbMATH DE number 3903221 |
Statements
A characterization of convolution and related operations (English)
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1985
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The author solves the functional equation: \((*)\quad \tau ((F+G)/2,H)=(\tau (F,H)+\tau (G,H))/2.\) Here F, G and H are arbitrary distribution functions and \(\tau\) is a triangle function to be found. The main result is the following theorem: Convolution is the unique continuous triangle function that satisfies the functional equation (*) and is in step with addition.
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distribution functions
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triangle function
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Convolution
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