On hermite interpolating L-2-approximants

We consider L-2-appoximation of a real-valued square integrable function by polynomials that satisfy certain Hermite interpolation conditions. The solution of the modified minimization problem is found by constructing an orthogonal basis of the underlying approximating subspace. A convergence problem related to the best approximants is considered in a restricted set-up. Some computational aspects based on discretization of the underlying measure are also discussed in detail.