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A note on d’Alembert’s functional equation. (English) Zbl 0991.39010

The author reproves the well known fact that the bounded, measurable and real-valued solutions of d’Alembert’s functional equation on \(\mathbb{R}^n\) are 0 and the functions \(x\to\cos \langle x,\xi\rangle\), \(x\in \mathbb{R}^n\), where \(\xi\) ranges over \(\mathbb{R}^n\). The new feature of the paper is that it uses the theory of almost-periodic functions in the proof.

MSC:

39B22 Functional equations for real functions
42A75 Classical almost periodic functions, mean periodic functions
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References:

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