The Convolution Type Equation on in Space of Functions those are Summed with Exponential Weights. Part 1

Abstract

In this paper (parts 1 and 2) the theory of one-sided invertibility of the convolution operator on R in space of functions those are summed with exponential weights is considered. In part 1 we present results on the boundedness of the convolution operator, the division theorem in the algebra of the analytic functions in the band and a Fredholm problem for Wiener-Hopf operator in studying space.