On the norms of the Dubuc-Deslauriers subdivision schemes
Conti et al. (2012, Remark 3.4) conjecture that the norm of the interpolatory 2n-point Dubuc-Deslauriers subdivision scheme is bounded from above by 4 for any n is an element of N. We disprove their conjecture by showing that the norm grows logarithmically in n and therefore diverges as n increases. (C) 2013 Elsevier B.V. All rights reserved.
subdivision interpolatory dubuc-deslauriers schemes