Dini–Lipschitz criterion
From HandWiki
In mathematics, the Dini–Lipschitz criterion is a sufficient condition for the Fourier series of a periodic function to converge uniformly at all real numbers. It was introduced by Ulisse Dini (1872), as a strengthening of a weaker criterion introduced by Rudolf Lipschitz (1864). The criterion states that the Fourier series of a periodic function f converges uniformly on the real line if
where is the modulus of continuity of f with respect to .
References
- Dini, Ulisse (1872), Sopra la serie di Fourier, Pisa, https://books.google.com/books?id=bCD\_SAAACAAJ
- Hazewinkel, Michiel, ed. (2001), "Dini-Lipschitz criterion", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Main_Page
![]() | Original source: https://en.wikipedia.org/wiki/Dini–Lipschitz criterion.
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