6. Various applications of Fourier series

6.1 Wirtinger inequality

This is an inequality linking the L ² norms of a function and its derivative; to be precise, we have the following proposition.

Proposition 4 (Wirtinger inequality).

Letb > 0 andybe a real-valued classC ¹ on [0, b], such that :

y (0) = y (b ) = 0.

Then : $\int_{0}^{b} y^{2} (t)$

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Various applications of Fourier series

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(1) - DAVIS (P.) - Interpolation and approximation.
(2) - KUIPERS (L.), NIEDERREITER (H.) - Uniform distribution of sequences. - Wiley-Interscience Series, 1974.
(3) - ZYGMUND (A.) - Trigonometric...

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