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.File allegato/i alla scheda:
| File | Dimensione del file | Formato | |
|---|---|---|---|
|
YJCOM1140-1.pdf
Solo gestori di archivio
Descrizione: publisher's version - versione dell'editore
Dimensione del file
435.54 kB
Formato
Adobe PDF
|
435.54 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
Aisberg ©2008 Servizi bibliotecari, Università degli studi di Bergamo | Terms of use/Condizioni di utilizzo
