Linear functional equations of the first, second, and third kind in $L_2$

Under consideration are the functional equations of the first, second, and third kind with operators in wide classes of linear continuous operators in $L_2$ containing all integral operators. We propose methods for reducing these equations by linear invertible changes either to linear integral equations of the first kind with nuclear operators or to equivalent linear integral equations of the second kind with quasidegenerate Carleman kernels. Some various approximate methods of solution are applicable to the so-obtained integral equations.