De la Vallée-Poussin criterion
From Encyclopedia of Mathematics
for pointwise convergence of a Fourier series
If a 
-periodic function 
which is integrable on the segment 
is such that the function 
defined by
 |
, is of bounded variation on some segment 
, then the Fourier series of 
converges at 
to the number
 |
The de la Vallée-Poussin criterion is stronger than the Dini criterion, the Dirichlet criterion (convergence of series), and the Jordan criterion. It was demonstrated by Ch.J. de la Vallée-Poussin [1].
References
| [1] | Ch.J. de la Vallée-Poussin, "Un nouveau cas de convergence des séries de Fourier" Rend. Circ. Mat. Palermo , 31 (1911) pp. 296–299 |
| [2] | N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian) |
How to Cite This Entry:
De la Vallée-Poussin criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=De_la_Vall%C3%A9e-Poussin_criterion&oldid=16429
De la Vallée-Poussin criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=De_la_Vall%C3%A9e-Poussin_criterion&oldid=16429
This article was adapted from an original article by B.I. Golubov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article