There exists a positive function ψ(t) on t ≥ 0, with fast decay at infinity, such that for every measurable set O in the Euclidean space and R > 0, there exist entire functions A(x) and B (x) of exponential type R, satisfying A(x) ≤ xω(x) ≤ B(x) and |B(x) - A(x)| ≤ψ (Rdist (x,θomega;)). This leads to Erd?os Turán 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. © 2010 American Mathematical Society.

Colzani, L., Gigante, G., & Travaglini, G. (2011). Trigonometric approximation and a general form of the Erdős-Turan inequality. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(2), 1101-1123 [10.1090/S0002-9947-2010-05287-0].

Trigonometric approximation and a general form of the Erdős-Turan inequality

COLZANI, LEONARDO;TRAVAGLINI, GIANCARLO
2011

Abstract

There exists a positive function ψ(t) on t ≥ 0, with fast decay at infinity, such that for every measurable set O in the Euclidean space and R > 0, there exist entire functions A(x) and B (x) of exponential type R, satisfying A(x) ≤ xω(x) ≤ B(x) and |B(x) - A(x)| ≤ψ (Rdist (x,θomega;)). This leads to Erd?os Turán 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. © 2010 American Mathematical Society.
No
Articolo in rivista - Articolo scientifico
Scientifica
Discrepancy; Erdős-Turán inequality;
English
1101
1123
23
Colzani, L., Gigante, G., & Travaglini, G. (2011). Trigonometric approximation and a general form of the Erdős-Turan inequality. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(2), 1101-1123 [10.1090/S0002-9947-2010-05287-0].
Colzani, L; Gigante, G; Travaglini, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/18701
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