A discrete approach to Wirtinger's inequality
Classical Analysis and ODEs
2019-05-17 v1 Differential Geometry
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 -periodic functions.
Cite
@article{arxiv.1905.05403,
title = {A discrete approach to Wirtinger's inequality},
author = {Julià Cufí and Agustí Reventós and Carlos J. Rodríguez},
journal= {arXiv preprint arXiv:1905.05403},
year = {2019}
}
Comments
9 pages