On the foundation of bases of spline spaces

摘要

The concept of foundation is a sharper concept than support which allows us to recognize spline bases suitable for design and computational purposes. We present new results on least founded bases of univariate spaces. In the case of tensor product spaces, we find under very general conditions bases of minimally founded functions although we show that, in contrast to the univariate case, they are no least founded bases. We also analyze related questions in a space of splines defined on angular regions of the plane.