Theorem 2 guarantees existence and uniqueness of the solution of the GLK equation only when the **data** f (t) belongs to the range of the operator of the forward problem, i.e. for the case of errorless data. However, in the realistic case of an error in the data, stability with respect to this error is not guaranteed by Theorem 2. Hence, the question about regularizing properties of GLK remains open. On the other hand, estimate (41) of Theorem 1 ensures stability of AGCM with respect to a small error in the data, and the same is true for the 3-d version of this method [6,9,25].