Summary.
Mean periodic functions play an important role in the theory of functional equations. Based on fundamental results on spectral synthesis it is possible to introduce a Fourier type transformation for mean periodic functions on the real line. This transformation can be used to solve convolution-type functional equations. It turns out that this transformation has a close relation to some kind of conditional expectation.
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Received: September 30, 1997; revised version: April 10, 1999.
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Székelyhidi, L. On mean periodic functions. Aequ. math. 58, 203–213 (1999). https://doi.org/10.1007/s000100050108
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DOI: https://doi.org/10.1007/s000100050108