Abstract
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.
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References
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Pavlov, A.V. Permutability of Cosine and Sine Fourier Transforms. Moscow Univ. Math. Bull. 74, 75–78 (2019). https://doi.org/10.3103/S0027132219020074
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DOI: https://doi.org/10.3103/S0027132219020074