On the solvability of bivariate Hermite-Birkhoff interpolation problems

摘要

In a recent paper by Hack (1987), certain bivariate polynomial Hermite-Birkhoff interpolation problems are considered and sufficient conditions for unique solvability are obtained by applying a general result on interpolation with tensor-functionals. In this paper, using a matricial approach and with the guideline of a result due to Stenger (1968), these conditions are shown to be also necessary and expressed in terms of the unisolvence of certain univariate interpolation problems. The results are valid not only for the polynomial case but also for interpolation with bivariate functions built from univariate extended complete Tchebycheff (ECT) systems.