On bivariate Birkhoff interpolation (Q1093109)

The author gives criteria for unique solvability of multivariate Birkhoff interpolation problems. To this end a method of \textit{W. Haussmann} type [see Math. Z. 124, 191-198 (1972; Zbl 0226.41007)] which interpolates with tensor-functionals is introduced. By this method the author deduces sufficient conditions for regularity of the two-dimensional incidence matrices which are used to describe the bivariate Birkhoff interpolation problems. The author's method covers all those results of multivariate interpolation deduced by Boolean methods and also permits solution of problems which cannot be investigated by Boolean methods.