d'Alembert's other functional equation (Q2834189)
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scientific article; zbMATH DE number 6656719
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | d'Alembert's other functional equation |
scientific article; zbMATH DE number 6656719 |
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d'Alembert's other functional equation (English)
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25 November 2016
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functional equation
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d'Alembert
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group
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compact group
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irreducible representation
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continuous complex-valued solutions
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The expression ``other functional equation'' refers to the functional equation NEWLINE\[NEWLINE f(x+y)-f(x-y)=2g(x)h(y)\tag{1} NEWLINE\]NEWLINE which was first studied by d'Alembert in connection with the problem of vibrating strings. In the paper, the authors investigate equation (\(1\)) in an abstract setting and find formulas for the continuous complex-valued solutions defined on a topological group generated by its squares and its center.
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