Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2  functions. The class of prox-regular functions covers all convex functions, lower C2  functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...

Although our proof is standard (essentially the same as presented by Serre [2], whose was the first account that I understood) we eschew complexvariable theory. Instead we use simple estimates from real-variable theory. Only one new difficulty is introduced: proving that L(1, χ) 6= 0 for nontrivial real-valued Dirichlet characters χ. We use an argument of Monsky [1] to prove this fact. Our argu...