A Refinement of the Two-Radius Theorem on the Bessel–Kingman Hypergroup

In the present paper, we study an equation of the form where , is the generalized Bessel translation operator, and is an even function locally integrable with respect to the measure on the interval . A description of the solutions of this equation in the form of series in special functions is obtained. Based on this result, we completely study the existence of a nonzero solution of a system of two such equations.