A discrete approach to wirtinger's inequality

Julià Cufí; Agustí Reventós; Carlos J. Rodríguez

doi:10.7153/jmi-2019-13-50

A discrete approach to wirtinger's inequality

Julià Cufí, Agustí Reventós, Carlos J. Rodríguez

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Resum

© 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.

Idioma original	Anglès
Pàgines (de-a)	737-746
Nombre de pàgines	10
Revista	Journal of Mathematical Inequalities
Volum	13
Número	3
DOIs	https://doi.org/10.7153/jmi-2019-13-50
Estat de la publicació	Publicada - 1 de gen. 2019

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10.7153/jmi-2019-13-50

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

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http://www.mendeley.com/research/discrete-approach-wirtingers-inequality

Com citar-ho

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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",

author = "Juli{\`a} Cuf{\'i} and Agust{\'i} Revent{\'o}s and Rodr{\'i}guez, {Carlos J.}",

year = "2019",

month = jan,

day = "1",

doi = "10.7153/jmi-2019-13-50",

language = "English",

volume = "13",

pages = "737--746",

journal = "Journal of Mathematical Inequalities",

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T1 - A discrete approach to wirtinger's inequality

AU - Cufí, Julià

AU - Reventós, Agustí

AU - Rodríguez, Carlos J.

PY - 2019/1/1

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

UR - http://www.mendeley.com/research/discrete-approach-wirtingers-inequality

U2 - 10.7153/jmi-2019-13-50

DO - 10.7153/jmi-2019-13-50

M3 - Article

SN - 1846-579X

VL - 13

SP - 737

EP - 746

JO - Journal of Mathematical Inequalities

JF - Journal of Mathematical Inequalities

IS - 3

ER -

A discrete approach to wirtinger's inequality

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