Exponential Monomials on Sturm--Liouville Hypergroups

Abstract

Using the concept of exponential monomial on Sturm--Liouville hypergroups we show that an important subclass of exponential monomials, the class of special exponential monomials has a linear independence property. The result can be reformulated as the linear independence of the derivatives with respect to the parameter of the solutions of eigenvalue problems for second order linear differential equations.