Difference between revisions of "De la Vallée-Poussin singular integral"
From Encyclopedia of Mathematics
Ulf Rehmann (talk | contribs) m (moved De la Vallée-Poussin singular integral to De la Vallee-Poussin singular integral: ascii title) |
Ulf Rehmann (talk | contribs) m (moved De la Vallee-Poussin singular integral to De la Vallée-Poussin singular integral over redirect: accented title) |
(No difference)
|
Revision as of 07:54, 26 March 2012
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=22329
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=22329
This article was adapted from an original article by P.P. Korovkin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article