A Muntz type theorem for a family of corner cutting schemes

摘要

Dimension elevation process of Gelfond-Bezier curves generates a family of control polygons obtained through a sequence of corner cuttings. We give a Muentz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the Muentz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the convergence of the corresponding dimension elevation algorithms.