On the polynomial hypergroups in one variable and some examples

The theory of hypergroups has been one of the basic themes in harmonic analysis andstudied by Dunkl [5], Jewett [10] and Spector [16] in 1970's. They have studied the propertiesof convolution, continuity of supports, existence of neutral element and involution. Kawada,Bose and Mesner have developed the earlier work of Frobenius on the discrete and finite hypergroups.Zeuner, Koornwinder, Trimeche and Annabi have worked on the several polynomialhypergroups. Berezanskii, Kalyuzhnyi, Dunkl [5], Jewett [10], Lasser [11] and Spector [16]worked on the variable polynomial hypergroups. This theses consists of five chapters. Thebasic definitions are given in the first chapter. Hypergroups and their properties are given inthe second chapter. Polynomial hypergroups are given in the third chapter. Polynomial hypergroupsin one variable are given in the fourth chapter and the last chapter is denoted to theexamples of polynomial hypergroups in one variable.