Linear equations with multiplicative operators in commutative algebras with logarithms

Abstract

Fundamental solutions in Leibniz algebras with logarithms have been constructed in [2]. In several applications operators under consideration inducing logarithmic mappings are either multiplicative or can be reduced by a substitution to multiplicative operators. So that, in the present paper we shall construct solutions for equations with multiplicative operators in commutative algebras (for the sake of brevity) and we shall apply this construction to discrete systems. The extensive bibliography of the subject can be found in [3].