Integral representation for exponentially bounded negative-definite functions on hypergroups

Integral representation for exponentially bounded negative–definite functions on hypergroups

R. Nasr–Isfahani

Abstract:The author has recently shown that a Bochner type theorem obtained by Bloom and Ressel for exponentially
bounded positive–definite functions on second countable commutative hypergroups is valid for all commutative
hypergroups X. Here an application of this result is made to give an integral representation for exponentially
bounded negative–definite functions on X.

Key words Exponentially bounded, hypergroup, negative–definite function, positive linear functional
MSC (2000) 43A35, 43A62