Euler-MacLaurin formulas via differential operators

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• 作者：Yohann Le Floch^a ; ^{ylefloch@post.tau.ac.il" class="auth_mail" title="E-mail the corresponding author} ; Á ; lvaro Pelayo^b ; ^{alpelayo@ucsd.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65B15 ; 41A58 ; 52B20
• 刊名：Advances in Applied Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：73
• 期：Complete
• 页码：99-124
• 全文大小：702 K

文摘

Recently there has been a renewed interest in asymptotic Euler–MacLaurin formulas, because of their applications to spectral theory of differential operators. Using elementary means, we recover such formulas for compactly supported smooth functions on intervals, polygons, and three-dimensional polytopes, where the coefficients in the asymptotic expansion are sums of differential operators involving only derivatives of the function in directions normal to the faces of the polytope. Our formulas apply to wedges of any dimension.