A Generalized Fourier Method for the System of First-Order Differential Equations with an Involution and a Group of Operators

Resumo

A mixed problem is considered for a differential equation with an involution and matrix potential. The method of similar operators is used to transform the differential operator defined by this equation into the orthogonal direct sum of finite-rank operators. A theorem is established, based on which an operator group is constructed to describe mild solutions of the problem at hand.