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arXiv · 1905.05403

A discrete approach to Wirtinger's inequality

Julià Cufí·Agustí Reventós·Carlos J. Rodríguez
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Abstract

Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger's inequality that also allows to study the case of equality. Moreover it leads in a natural way to the Fourier series development of $2\pi$-periodic functions.

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Julià Cufí, Agustí Reventós, Carlos J. Rodríguez. 2019-05-14. A discrete approach to Wirtinger's inequality. https://doi.org/10.7153/jmi-2019-13-50

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