Localization principle
From Encyclopedia of Mathematics
For any trigonometric series with coefficients tending to zero, the convergence or divergence of the series at some point depends on the behaviour of the so-called Riemann function in a neighbourhood of this point.
The Riemann function 
of a given trigonometric series
 |
is the result of integrating it twice, that is,
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There is a generalization of the localization principle for series with coefficients that do not tend to zero (see [2]).
References
| [1] | N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian) |
| [2] | A. Zygmund, "Trigonometric series" , 1 , Cambridge Univ. Press (1988) |
How to Cite This Entry:
Localization principle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Localization_principle&oldid=33324
Localization principle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Localization_principle&oldid=33324
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article