The Sobolev-type moment problem

We propose necessary and sufficient conditions for a bisequence of complex numbers to be a moment one of Sobolev type over the real line, the unit cir cle and the complex plane. We achieve this through converting the moment pr oblem in question into a matrix one and utilizing some techniques coming fr om operator theory. This allows us to consider the Sobolev type moment prob lem in its full generality, not necessarily in the diagonal case and even o f infinite order.