On Fourier Re-Expansions
On Fourier Re-Expansions
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关于傅里叶再展开
DOI：
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发表时间：
2012
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通讯作者：
E. Liflyand
中科院分区：
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作者：
E. Liflyand
将一个关于绝对收敛的余弦(正弦)傅里叶级数的重展开式绝对收敛的老问题推广到非周期情形(傅里叶变换)。给出了傅里叶变换与它们的希尔伯特变换之间的关系的充要条件。得到了Hilbert变换可积的充分条件。
An old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series is extended to the non-periodic case (Fourier transforms). Necessary and sufficient conditions are given as relations between the Fourier transforms and their Hilbert transforms. Sufficient conditions for integrability of the Hilbert transform are obtained.