On exponentially bounded positive-definite functions on hypergroups (Q5943644)

In this note, Bochner's theorem is proved for exponentially bounded positive definite functions on commutative hypergroups. In the case of second countability, the result was already shown by W. R. Bloom and P. Ressel, and for multiplicative absolute values as bounds, the result immediately follows from the renormalization procedure of the reviewer and Bochner's theorem for bounded positive definite functions; see [\textit{M. Voit}, Math. Z. 198, 405-421 (1988; Zbl 0677.43002)].