Operational calculus and differential equations with infinitely smooth coefficients

Abstract

A subring MF of the field of Mikusiński operators is constructed as a countable union space. Some topological properties of MF are investigated. Then, the product of an infinitely differentiable function and an element of MF is given and is used to investigate operational equations with infinitely smooth coefficients.

Keywords

• Mikusiński operator
• infinitely differentiable
• operational equation.