Sard kernel theorems and interpolation remainder theory on perpendicular parallelepipeds (Q1059806)

The authors generalize the Sard type Taylor expansion to functions of three variables on perpendicular parallelepipeds. In its definition positive and negative orientation is to be distinguished. With rather complicated notation, which is hardly avoidable, sufficient conditions for the existence of Sard type Taylor expansion are formulated. Kernel theorems are proved and error bounds for interpolation operators on perpendicular parallelepipeds are derived. The scarce comments and very complicated formulae make it difficult to follow the authors' basic idea without comparison with some results in the references.