Gibbs’ phenomenon and surface area
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- by L. de Michele and D. Roux PDF
- Proc. Amer. Math. Soc. 134 (2006), 3561-3566 Request permission
Abstract:
If a function $f$ is of bounded variation on $T^N\ (N\geq 1)$ and $\{{\varphi }_n\}$ is a positive approximate identity, we prove that the area of the graph of $f*{\varphi }_n$ 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.References
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Additional Information
- L. de Michele
- Affiliation: Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, via R. Cozzi 53, 20126 Milano, Italia
- D. Roux
- Affiliation: Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, via R. Cozzi 53, 20126 Milano, Italia
- Received by editor(s): June 21, 2005
- Published electronically: May 31, 2006
- Communicated by: Michael T. Lacey
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 3561-3566
- MSC (2000): Primary 42B99
- DOI: https://doi.org/10.1090/S0002-9939-06-08639-4
- MathSciNet review: 2240668