Formal product of trigonometric series
From Encyclopedia of Mathematics
 |
The series
 |
where
 |
If 
as 
, 
, and if
 |
has sum 
, then the series
 |
has sum zero uniformly on 
. The condition
 |
is satisfied if, for example,
 |
is the Fourier series of a three-times differentiable function 
.
References
| [1] | N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian) |
| [2] | A. Zygmund, "Trigonometric series" , 1–2 , Cambridge Univ. Press (1988) |
How to Cite This Entry:
Formal product of trigonometric series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Formal_product_of_trigonometric_series&oldid=17751
Formal product of trigonometric series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Formal_product_of_trigonometric_series&oldid=17751
This article was adapted from an original article by T.P. Lukashenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article