摘要

We analyse the mask associated with the 2n-point interpolatory Dubuc-Deslauriers subdivision scheme S-a[n]. Sharp bounds are presented for the magnitude of the coefficients a(2i-1)([n]) of the mask. For scales i is an element of [1, root n] it is shown that vertical bar a(2i-1)([n])vertical bar is comparable to i(-1), and for larger power scales, exponentially decaying bounds are obtained. Using our bounds, we may precisely analyse the summability of the mask as a function of n by identifying which coefficients of the mask contribute to the essential behaviour in n, recovering and refining the recent result of Deng-Hormann Zhang that the operator norm of S-a[n] on l(infinity) grows logarithmically in n.

  • 出版日期2014

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