On the L∞L∞-norm of the orthogonal projector onto splines. A short proof of A. Shadrin’s theorem

The existence of a bound for the L∞L∞-norm of the orthogonal projector onto splines, depending on the degree of splines, but independent of the mesh, was a long-standing conjecture by Carl de Boor. Finally, A. Yu. Shadrin solved it in 2001, but his proof is rather long and complicated. It is the purpose of this paper to present an alternative–short and simple–proof.