Difference between revisions of "Hardy-Littlewood criterion"
From Encyclopedia of Mathematics
(Importing text file) |
Ulf Rehmann (talk | contribs) m (moved Hardy–Littlewood criterion to Hardy-Littlewood criterion: ascii title) |
(No difference)
| |
Revision as of 18:52, 24 March 2012
for the convergence of a Fourier series
If a 
-periodic function 
is such that
 |
and if its Fourier coefficients 
satisfy the conditions
 |
for some 
, then the Fourier series of 
at 
converges to 
.
The criterion was established by G.H. Hardy and J.E. Littlewood [1].
References
| [1] | G.H. Hardy, J.E. Littlewood, "Some new convergece criteria for Fourier series" J. London. Math. Soc. , 7 (1932) pp. 252–256 |
| [2] | N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian) |
How to Cite This Entry:
Hardy-Littlewood criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hardy-Littlewood_criterion&oldid=15991
Hardy-Littlewood criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hardy-Littlewood_criterion&oldid=15991
This article was adapted from an original article by B.I. Golubov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article