Recovery of functions, their derivatives, and supports given the moment sequence of underlying functions

The problem of recovering functions given incomplete information contained in the sequence of their moments or the values of Laplace transforms represents special case of the so-called ill-posed problem. Several approximations and corresponding upper bounds for the uniform and L1-rates of convergences are derived.  Applications in computed tomography and statistics including the problem of recovering the derivatives, and the support of function will be outlined. In particular, reconstruction of a function from the values of its Radon transform (projections) will be discussed as well.