On Fourier re-expansions
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🧮 math.CA
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fouriertransformscosineseriessineabsoluteabsolutelycertain
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We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
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