Title：Moment functions and Exponential monomials on hypergroup Joins
Speaker：Kedumetse Vati
Time：16:00-17:00, September28
Location：Zoom, Zoom Meeting ID: 976 1418 4288, Password: 104318
Abstract：The study of the theory of hypergroups is one of the important directions of researches on modern mathematics. In this talk, we mainly study some problems about hypergroups (especially hypergroup join) and related functional equations and spectral synthesis.
Moment functions, Exponential monomials and polynomials are the basic building blocks of spectral synthesis. Recently, a systematic study of monomials has been started on hypergroups, we joined the investigation of this issue too. We extend our study on hypergroups and hypergroup joins to the exponential monomials and obtain some results. We showed that every nonzero generalized exponential monomial on a compact commutative hypergroup is of degree zero. We proved that every generalized 1–exponential monomial on a compact hypergroup is constant, which also gives a positive answer to the open problem if every 1–sine function is zero on non-commutative compact hypergroups. Moreover, we found two equivalent descriptions of generalized exponential monomial of degree at most n on a hypergroup join. In addition, a natural generalization of moment function can be defined on hypergroups which leads to the concept of generalized moment function sequences. Hence we furthermore described some generalized moment function sequences and their related properties on hypergroup joins.
