Point derivations on the $L^1$-algebra of polynomial hypergroups
We investigate whether the $L^1$-algebra of polynomial hypergroups has non-zero bounded point derivations. We show that the existence of such point derivations heavily depends on growth properties of the Haar weights. Many examples are studied in detail. We can thus demonstrate that the $L^1$-algebras of hypergroups have properties (connected with amenability) that are very different from those of groups.