Sturm-liouville hypergroups

In this thesis, which has four section, one dimensional hypergroups on the half lineand on the compact intervals will be constructed. We shall perform the construction insome details on the half line and only quote the corresponding results for the compact case.It turns out that all known examples of hypergroups on R+ arise from Sturm Liouville(SL)boundary value problems over R+ where the solutions coincide with the characters ofhypergroup being constructed. The convolutions generated in this way clearly depend on thefunction defining the underlying Sturm Liouville operator. Its geometric algebraic propertiesare suitable means to classify Sturm Liouville convolutions on R+.5