An integral equation of convolution type with two kernels and its abstract analog

We consider an integral equation of the convolution type with two kernels, generated by functions from some Banach algebras, and a linear equation with two coefficients in abstract rings with factorial pairs of sub-rings. Theorems and formulas have been proved, characterizing the general relation of the solvability problem of the equations with the factorization properties of elements constructed from the kernels and coefficients.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1065–1078, August, 1992.