Projection operators onto spaces of Chebyshev splines

TL;DR

This paper proves that orthogonal projection operators onto Chebyshev spline spaces are uniformly bounded in the supremum norm, ensuring stability and robustness of these projections in approximation tasks.

Contribution

The paper establishes the uniform boundedness of Chebyshev spline orthoprojectors on L-infinity, a key property for their effective use in approximation theory.

Findings

Orthoprojectors are uniformly bounded on L-infinity.

Ensures stability of Chebyshev spline projections.

Supports their application in approximation and numerical analysis.

Abstract

We prove that the Chebyshev spline orthoprojectors are uniformly bounded on $L^\infty$.