It is proved that the cosine and sine Fourier transforms are permutable with the opposite sign on the positive real axis. This property implies that the cosine and sine Fourier transforms coincide in absolute value on the semiaxis for a wide class of functions.

中文翻译：

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余弦和正弦傅立叶变换的置换性

证明了余弦和正弦傅立叶变换是可置换的，在正实轴上具有相反的符号。此属性表示对于一类广泛的函数，余弦和正弦傅立叶变换的绝对值在半轴上重合。