Semigroup Classification and Gelfand–Shilov Classification of Systems of Partial Differential Equations

Resumo

Two approaches to systems of linear partial differential equations are considered: the traditional approach based on the generalized Fourier transform and the semigroup approach, under which the system is considered as a particular case of an operator-differential equation. For these systems, the semigroup classification and the Gelfand–Shilov classification are compared.