Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval
A convolution equation is considered in the Beurling space of ultradifferentiable functions of mean type on an interval. The author completely describes conditions under which the convolution equation has a solution. As a particular case, infinite-order differential equations with constant coefficients are considered. Necessary and sufficient conditions of solvability of such equations are established. Some examples illustrate the theory.
Beurling type ultradifferentiable functions
scientific article; zbMATH DE number 6105689
scientific article