On interpolation of polynomial operators (Q1364057)

In this paper the authors construct an operator interpolant for a polynomial operator on an orthonormal system of knots in a Hilbert space. For the construction of this interpolant, the authors generalize at the operator level the method of orthogonal moments, which is used in problems of identification of a polynomial functional system with subsequent application of the scheme for separation of homogeneous functions. The interpolant accuracy is then estimated for the constructed interpolant; for the case when the orthonormal system of knots is a basis of the space, the accuracy bound leads to pointwise convergence of the operator interpolation process as the number of knots increases. Such a convergence example is considered for a regular functional polynomial of second degree defined on periodic functions whose derivatives are of bounded variation. (from the authors' introduction to the paper).