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Author Colzani, Leonardo ♦ Gigante, Giacomo ♦ Travaglini, Giancarlo
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2010-01-06
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Number Theory ♦ Mathematics - Classical Analysis and ODEs ♦ 11K38 ♦ 42C15 ♦ math
Abstract There exists a positive function $\psi(t)${on}$t\geq0${, with fast decay at infinity, such that for every measurable set}$\Omega${in the Euclidean space and}$R>0${, there exist entire functions}$A(x) ${and}$B(x) ${of exponential type}$R${, satisfying\}$A(x)\leq \chi_{\Omega}(x)\leq B(x)${and}$ B(x)-A(x) \leqslant\psi(R\operatorname*{dist}(x,\partial\Omega)) $. This leads to Erd\H{o}s Tur\'{a}n estimates for discrepancy of point set distributions in the multi dimensional torus. Analogous results hold for approximations by eigenfunctions of differential operators and discrepancy on compact manifolds.
Educational Use Research
Learning Resource Type Article


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