On One Integral Equation in the Theory of Transform Operators

Abstract

Integral representations of solutions of one differential equation with singularities in the coefficients, containing the Bessel operator perturbed by some potential, are considered. The existence of integral representations of a certain type for such solutions is proved by the method of successive approximations using transform operators. Potentials with strong singularities at the origin are allowed. As compared with the known results, the Riemann function is expressed not via the general hypergeometric function, but, more specifically, via the Legendre function, which helps to avoid unknown constants in the estimates.