Exponentially convex functions on hypercomplex systems (Q554797)

Summary: A hypercomplex system (h.c.s.) \(L_1(Q, m)\) is, roughly speaking, a space which is defined by a structure measure \(c(A, B, r)\), \(A, B \in \mathcal B(Q)\). Such spaces were studied by \textit{Yu. M. Berezanskiĭ} and \textit{S. G. Kreĭn} [Ukr. Mat. Zh. 3, 184--204 (1951; Zbl 0045.38302)]. Our main goal is to define exponentially convex functions (e.c.f.) on (h.c.s.) and to study their properties. The definition of such functions is a natural generalization of the definition on semigroups.