On one class of differential operators and their application

Abstract

We use a generalized differentiation operator to construct a generalized shift operator, which makes it possible to define a generalized convolution operator in the space H(ℂ). Next, we consider the characteristic function of this operator and introduce a generalized Laplace transform. We study the homogeneous equation of the generalized convolution operator, investigate its solvability, and consider the multipoint Vallee Poussin problem.