for the convergence of Fourier series
If a -periodic function has bounded variation on the interval , then its Fourier series converges at every point to ; if, in addition, is continuous on , then its Fourier series converges to it uniformly on every interval strictly inside . The criterion was established by C. Jordan ; it generalizes the Dirichlet theorem on the convergence of Fourier series of piecewise-monotone functions.
|||C. Jordan, "Sur la série de Fourier" C.R. Acad. Sci. Paris , 92 (1881) pp. 228–230|
|||N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian)|
The Jordan criterion is also called the Dirichlet–Jordan test, cf. [a1].
|[a1]||A. Zygmund, "Trigonometric series" , 1–2 , Cambridge Univ. Press (1988)|
Jordan criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Jordan_criterion&oldid=17285