  We study three well-known minimization problems in Hilbert spaces: the
weighted least squares problem and the related problems of abstract splines and
smoothing. In each case we analyze the solvability of the problem for every
point of the Hilbert space in the corresponding data set, the existence of an
operator that maps each data point to its solution in a linear and continuous
way and the solvability of the associated operator problem in a fixed
p-Schatten norm.
