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=46956
Formal product of trigonometric series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Formal_product_of_trigonometric_series&oldid=46956
This article was adapted from an original article by T.P. Lukashenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article