Unique Solvability of a Functional-Differential Equation with Orthotropic Contractions in Weighted Spaces

Abstract

We study the solvability of a new class of functional-differential equations with transformations of the arguments of the unknown function. The transformations include contractions in one independent variable and dilations in the other. (We refer to such transformations as orthotropic contractions.) Sufficient conditions for the solvability of such equations in weighted spaces are obtained depending on the exponent of the space. We show that the original problem reduces to the study of a certain finite-difference equation in the space L²(ℝ).