If a function f is of bounded variation on T<sup>N</sup> (N ≥ 1) and {φ<sub>n</sub>} is a positive approximate identity, we prove that the area of the graph of f * φ<sub>n</sub> converges from below to the relaxed area of the graph of f. Moreover we give asymptotic estimates for the area of the graph of the square partial sums of multiple Fourier series of functions with suitable discontinuities. ©2006 American Mathematical Society.

DE MICHELE, L., Roux, D. (2006). Gibbs' phenomenon and surface area. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134(12), 3561-3566 [10.1090/S0002-9939-06-08639-4].

Gibbs' phenomenon and surface area

DE MICHELE, LEONEDE;
2006

Abstract

If a function f is of bounded variation on TN (N ≥ 1) and {φn} is a positive approximate identity, we prove that the area of the graph of f * φn converges from below to the relaxed area of the graph of f. Moreover we give asymptotic estimates for the area of the graph of the square partial sums of multiple Fourier series of functions with suitable discontinuities. ©2006 American Mathematical Society.
Articolo in rivista - Articolo scientifico
Harmonic analysis,Gibbs phenomenon
English
2006
134
12
3561
3566
none
DE MICHELE, L., Roux, D. (2006). Gibbs' phenomenon and surface area. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134(12), 3561-3566 [10.1090/S0002-9939-06-08639-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/11470
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