A Muntz Type Theorem for a Family of Corner Cutting Schemes
arXiv:1111.3410
Abstract
By identifying a family of corner cutting schemes as a dimension elevation process of Gelfond-Bezier curves, we give a Muntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the Muntz 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.
20 pages, 6 figures. Submitted manuscript v2, corrected typo in formula 2