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arXiv 1003.5747math.CA
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关于函数的傅立叶级数继续单模

Sur les séries de Fourier des fonctions continues unimodulaires

Jean Bourgain, Jean-Pierre Kahane

摘要:

具有常数绝对值的连续函数的傅里叶级数具有有趣的性质:根据本文的主要定理,如果具有正指数的系数关于某个权重(指数的任何实正幂)是平方可和的,则对于负指数也是如此。该结果推广到VMO,而不推广到有界可测函数.

英文摘要:

The Fourier series of continuous functions of constant absolute value have interesting properties : according to the main theorems of the article, if the coefficients with positive indexes are square-summable with respect to a certain weight (any real positive power of the index), the same is true for negative indexes. The result extends to VMO and does not to bounded measurable functions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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