In the present paper we investigate Moore-Penrose inverse and characteristic matrix of unbounded WCT operators on the Hilbert space $L^2(\mu)$. Also, we obtain some applications of the Moore-Penrose inverse of unbounded operators on the Hilbert space $\mathcal{ H}$ to variational regularization problem. Moreover,some examples are provided to illustrate the applications of our results in linear equations and specially Fredholm integral equations.
Categories: math.FA math.OA