The adjoint Riemann-Stieltjes integral (Q2479658)

The author gives the family of solutions of a differential equation in a generalized form. First the algebra of discontinuous functions defined on a real segment is introduced and main topological properties are mentioned. The algebras of discontinuous functions are commutative Banach algebras with the unit element and the adjoint multiplication and integral are defined in these spaces. The theorem which gives the family of solutions is applied in the case of the impulse equation which is written in terms of the traditional generalized functions.