A matrix modification of formulas for the Hermite interpolation of operators in a Hilbert space

Abstract

Vychisl. Prikl. Mat., No. 78, 38-48 (1994)) dimension are derived. Bibliography: 3 titles.The paper is devoted to further extension of the results of [1] concerning the construction of necessary and sufficient conditions for the existence of an Hermite operator polynomial, aswell as to the description of the whole set of such interpolasxts in a Hilbert space. However, in contrast to [1], the main formulas of this paper involve vectors and matrices of lower dimension. This concerns both the solvability conditions for the interpolation problem and interpolational formulas. The solvability conditions in [1] are proved to be equivalent to the conditions obtained in this paper.Let X be a Hilbert and Y be a vector space. At nodes xi E X the values of an operator F: X -4 Y and