A discrete approach to wirtinger's inequality

Julià Cufí, Agustí Reventós, Carlos J. Rodríguez

Research output: Contribution to journalArticleResearch


© 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 languageEnglish
Pages (from-to)737-746
Number of pages10
JournalJournal of Mathematical Inequalities
Issue number3
Publication statusPublished - 1 Jan 2019


  • Fourier series
  • Piece-wise linear functions
  • Wirtinger's inequality


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