Uniqueness theorem for one class of pseudodifferential equations

Abstract

The uniqueness of solutions for homogeneous equations in the class of analytic functionals $Z^{\text{'}}\left({ℝ}^n\right)$ with pseudodifferential operators commuting under shifts is discussed. We establish conditions for the symbols of operators that allow one to partition this class of operators into equivalence classes in such a way that within each class, any condition of the regularity of solutions at infinity that guarantees the uniqueness of a solution for an equation with some representative of this class, also guarantees the uniqueness of a solution for equations with all representatives of the same class.