Integral functional equations on locally compact groups with involution (Q329390)
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scientific article; zbMATH DE number 6642204
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integral functional equations on locally compact groups with involution |
scientific article; zbMATH DE number 6642204 |
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Integral functional equations on locally compact groups with involution (English)
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21 October 2016
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The main theorem of the paper gives the solutions of the following functional equation: \[ f(x\sigma(y))+f(\tau(y)x)=2f(x)g(y),\qquad x,y\in M, \] where \(M\) is a group or a monoid, \(\sigma,\tau: M\to M\) are involutive automorphisms, and \(f,g: M\to\mathbb{C}\) are the unknown functions.
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functional equation
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involutive automorphism
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monoid
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multiplicative function
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locally compact groups
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