Poletaev G. S.
Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1077-1088
For an arbitrary operator, we pose a general reconstruction problem inverse to the problem of finding solutions. For the pair operator considered, this problem is reduced to the equivalent problem of reconstruction of the kernels of the pair integral equation of the convolution type that generates this operator. In the cases investigated, we prove theorems that characterize the reconstruction of the corresponding kernels, which are constructed in terms of two functions from different Banach algebras of the type L 1(−∞, ∞) with weight.
Ukr. Mat. Zh. - 1992. - 44, № 8. - pp. 1065–1078
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.
Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1213–1231
Ukr. Mat. Zh. - 1991. - 43, № 6. - pp. 803-813