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

Producción científica: Contribución a una revista › Artículo › Investigación

Resumen

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	Inglés
Páginas (desde-hasta)	737-746
Número de páginas	10
Publicación	Journal of Mathematical Inequalities
Volumen	13
N.º	3
DOI	https://doi.org/10.7153/jmi-2019-13-50
Estado	Publicada - 1 ene 2019

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

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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.\}",

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AU - Rodríguez, Carlos J.

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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

UR - https://www.scopus.com/pages/publications/85073209127

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DO - 10.7153/jmi-2019-13-50

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JO - Journal of Mathematical Inequalities

JF - Journal of Mathematical Inequalities

IS - 3

ER -

A discrete approach to wirtinger's inequality

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