Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8734The Convolution Type Equation on in Space of Functions those are Summed with Exponential Weights. Part 1DybinV BКафедра алгебры и дискретной математики; Южный федеральный университет; Southern Federal Universityvladimir-dybin@yandex.ruSouthern Federal University150220112162708092016Copyright © 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 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.convolution operatorsymbolweight spaceFredholm propertyоператор свёрткисимволвесовое пространствофредгольмовость