ON TWO-DIMENSIONAL POLYNOMIAL INTERPOLATION

A tuple of positive integers with is said to be regular if there exists a set such that the Hermite interpolation problem is regular, i.e., for arbitrary numbers , , , there exists a unique polynomial such that In this paper an algorithm is obtained that completely describes the regular and singular tuples under the condition that . In the case when only the derivatives of order are interpolated, necessary and sufficient conditions are obtained for an arbitrary tuple to be regular.Bibliography: 9 titles.