Sine functions on hypergroups

TL;DR

This paper extends the concept of sine functions from commutative hypergroups to various types of hypergroups, including non-commutative ones, providing a comprehensive description of these functions across different hypergroup structures.

Contribution

It generalizes sine functions to a broader class of hypergroups, including polynomial, Sturm–Liouville, and non-commutative hypergroups, expanding the theoretical framework.

Findings

Sine functions characterized on polynomial hypergroups

Description of sine functions on Sturm–Liouville hypergroups

Extension to non-commutative hypergroups

Abstract

In a recent paper we introduced sine functions on commutative hypergroups. These functions are natural generalizations of those functions on groups which are products of additive and multiplicative homomorphisms. In this paper we describe sine functions on different types of hypergroups, including polynomial hypergroups, Sturm--Liouville hypergroups, etc. A non-commutative hypergroup is also considered.