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Hypergroups are locally compact spaces with a group-like structure on which the bounded measures admit a convolution similar to that on a locally compact group. Important examples of hypergroups are double coset spaces, conjugacy spaces and duals of compact groups and also orbit spaces of certain locally compact groups. Moreover, the sets Z_{+} , R_{+} of nonnegative integers and reals respectively, the unit interval I and the unit disk D are also hypergroups with special operations different from the usual semigroup operations. In fact, a hypergroup K can be viewed as a probabilistic structure in the sense that to each pair x, y of points in K there exists a probability measure \epsilon_{X}^{*}\epsilon_{\mathcal{Y}} on K with compact support such that

Convolution semigroups of local type on a commutative hypergroup