On invertibility of A linear operator connected with singular differential equations
In this paper a representations of inverse and right inverse operators for operator of the form I + kC <sub>a</sub> on the Lebesgue space L <sub>2</sub> were obtained. Here I - identity operator and C <sub>a</sub> generalized Cesaro operator, k - real parameter. Such operator appears while studying various singular differential equations. The results can be used to study boundary value problems for singular differential equations, including the study of the asymptotic behavior of solutions.