General elementary solution of a 𝑞-sided convolution type homogeneous equation

Abstract

Exponential polynomials satisfying a homogeneous equation of convolution type are called its elementary solutions. The article is devoted to convolution-type operators in the complex domain that generalize the well-known operators of q q -sided convolution and π \pi -convolution. The properties of such operators are investigated and the general form of elementary solutions (general elementary solution) of a homogeneous equation of q q -sided convolution type is described.