A discrete approach to wirtinger's inequality

Julià Cufí; Agustí Reventós; Carlos J. Rodríguez

doi:https://doi.org/10.7153/jmi-2019-13-50

A discrete approach to wirtinger's inequality

Julià Cufí, Agustí Reventós, Carlos J. Rodríguez

Department of Mathematics

Research output: Contribution to journal › Article › Research

Abstract

© ELEMENT, Zagreb. 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 2π -periodic functions.

Original language	English
Pages (from-to)	737-746
Journal	Journal of Mathematical Inequalities
Volume	13
DOIs	https://doi.org/10.7153/jmi-2019-13-50
Publication status	Published - 1 Jan 2019

Keywords

Fourier series
Piece-wise linear functions
Wirtinger's inequality

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https://doi.org/10.7153/jmi-2019-13-50

https://ddd.uab.cat/record/224176

Cite this

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title = "A discrete approach to wirtinger's inequality",

abstract = "{\textcopyright} ELEMENT, Zagreb. 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 2π -periodic functions.",

keywords = "Fourier series, Piece-wise linear functions, Wirtinger's inequality",

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AU - Reventós, Agustí

AU - Rodríguez, Carlos J.

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Y1 - 2019/1/1

N2 - © ELEMENT, Zagreb. 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 2π -periodic functions.

AB - © ELEMENT, Zagreb. 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 2π -periodic functions.

KW - Fourier series

KW - Piece-wise linear functions

KW - Wirtinger's inequality

U2 - https://doi.org/10.7153/jmi-2019-13-50

DO - https://doi.org/10.7153/jmi-2019-13-50

M3 - Article

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EP - 746

JO - Journal of Mathematical Inequalities

JF - Journal of Mathematical Inequalities

SN - 1846-579X

ER -

A discrete approach to wirtinger's inequality

Abstract

Keywords

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