Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8672The Convolution Type Equation on R in Space of Functions those are Summed with Exponential Weights. Part 2DybinV BКафедра алгебры и дискретной математики; Южный федеральный университет; Southern Federal Universityvladimir-dybin@yandex.ruSouthern Federal University150320113394808092016Copyright © 2011,2011In 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 2 a I.A. Feldman construction providing the solution of a Fredholm problem for the considered convolution operator is contained. After the results of the invertibility (two-, left- and right-sided) of this operator are represented. The description of its defect subspaces and the constructions of its inverse operators is given.convolution operatorsymbolweight spaceinvertibilitydefect subspacesоператор свёрткисимволвесовое пространствофредгольмовостьобратимость