The classical Koksma–Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma–Hlawka type inequality which applies to piecewise smooth functions fχ_Ω, with f smooth and Ω a Borel subset of [0,1]^d. We state similar results with variation and discrepancy measured by Lp and Lq norms, 1/p+1/q=1, and we also give extensions to compact manifolds.

On the Koksma-Hlawka inequality

BRANDOLINI, Luca;GIGANTE, Giacomo;
2013-01-01

Abstract

The classical Koksma–Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma–Hlawka type inequality which applies to piecewise smooth functions fχ_Ω, with f smooth and Ω a Borel subset of [0,1]^d. We state similar results with variation and discrepancy measured by Lp and Lq norms, 1/p+1/q=1, and we also give extensions to compact manifolds.
journal article - articolo
2013
Brandolini, Luca; Colzani, Leonardo; Gigante, Giacomo; Travaglini, Giancarlo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/27970
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