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A sharp discrete convolution sum estimate
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DOI：10.1016/j.cnsns.2022.106923.png)
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Abstract
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The paper by C. Lubich in Numer. Math. 2(52):129-145, 1988 is widely cited for its analysis of convolution quadrature rules for integrals with weakly singular kernels. This analysis depends on a key technical lemma (an upper bound on a discrete convolution sum) whose proof uses some advanced tools. In the present paper it will be shown that this lemma can be quickly proved in an elementary way; moreover, the new proof includes those cases that were excluded from the 1988 paper, and the bounds obtained are shown to be sharp.(c) 2022 Elsevier B.V. All rights reserved.
Keywords:
Discrete convolution sum
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