On the value of the max-norm of the orthogonal projector onto splines with multiple knots

The supremum over all knot sequences of the max-norm of the orthogonal spline projector is studied with respect to the order k of the splines and their smoothness. It is first bounded from below in terms of the max-norm of the orthogonal projector onto a space of incomplete polynomials. Then, for continuous and for differentiable splines, its order of growth is shown to be k. Key words: Orthogonal projectors, Splines

• Type: Journal
• Year: 2006
• Where: JAT
• Authors: Simon Foucart
• Keywords: Incomplete Polynomials, JAT 2006, Orthogonal Projectors, Orthogonal Spline Projector