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 |
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Pages (from-to) | 737-746 |
Journal | Journal of Mathematical Inequalities |
Volume | 13 |
DOIs | |
Publication status | Published - 1 Jan 2019 |
Keywords
- Fourier series
- Piece-wise linear functions
- Wirtinger's inequality