Asymptotic Euler-Maclaurin formula over lattice polytopes

研究成果: Article査読

4 被引用数 (Scopus)

抄録

Formulas for the Riemann sums over lattice polytopes determined by the lattice points in the polytopes are often called Euler-Maclaurin formulas. An asymptotic Euler-Maclaurin formula, by which we mean an asymptotic expansion formula for Riemann sums over lattice polytopes, was first obtained by Guillemin and Sternberg (2007) [11]. Then, the problem is to find a concrete formula for each term of the expansion. In this paper, an asymptotic Euler-Maclaurin formula of the Riemann sums over general lattice polytopes is given. The formula given here is an asymptotic form of the so-called local Euler-Maclaurin formula of Berline and Vergne (2007) [3]. For Delzant polytopes, our proof given here is independent of the local Euler-Maclaurin formula. Furthermore, a concrete description of differential operators which appear in each term of the asymptotic expansion for Delzant lattice polytopes is given. By using this description, when the polytopes are Delzant lattice, a concrete formula for each term of the expansion in two dimension and a formula for the third term of the expansion in arbitrary dimension are given.

本文言語English
ページ(範囲)501-540
ページ数40
ジャーナルJournal of Functional Analysis
260
2
DOI
出版ステータスPublished - 2011 1月 15
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ASJC Scopus subject areas

  • 分析

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