A Müntz type theorem for a family of corner cutting schemes

Dimension elevation process of Gelfond–Bézier curves generates a family of control polygons obtained through a sequence of corner cuttings. We give a Müntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the Müntz 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.

► Identify a family of corner cutting schemes as dimension elevation process of Gelfond–Bézier curves.
► Give a Müntz type condition for the convergence of the dimension elevated control polygons to the underlying curve.
► Discuss the emergence of the Müntz condition in the problem and its possible implications for the density of infinite nested Chebyshev spaces.