De la Vallée-Poussin singular integral
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
An integral of the form
 |
(see also de la Vallée-Poussin summation method). The sequence 
converges uniformly to 
for functions 
which are continuous and 
-periodic on 
[1]. If
 |
at a point 
, then 
as 
. The following equality is valid [2]:
 |
References
| [1] | G.H. Hardy, "Divergent series" , Clarendon Press (1949) |
| [2] | I.P. Natanson, "Constructive function theory" , 1 , F. Ungar (1964) (Translated from Russian) |
Comments
The notation 
stands for 
(
terms), and 
(also 
terms). Thus,
 |
How to Cite This Entry:
De la Vallée-Poussin singular integral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=De_la_Vall%C3%A9e-Poussin_singular_integral&oldid=16238
De la Vallée-Poussin singular integral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=De_la_Vall%C3%A9e-Poussin_singular_integral&oldid=16238
This article was adapted from an original article by P.P. Korovkin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article