On the embedding of minimal spline spaces (Q5954717)

The author shows that a set of minimal \(m\)-degree spline spaces considered on a sequence of twice-refined uniform grids can be decomposed into the chains of spaces, in which every next space contains the preceding one. These chains are mutually disjoint, the spaces in one chain possess the same smoothness, and their generating splines uniformly tend to the \(B\)-spline in the direction toward the grid enlargement.