Novel definition preserves real function properties and proves the inversion theorem for Fourier transforms.
We propose a novel definition of Fourier transform, with the property that the transform of a real function is again a real function (without doubling the number of real components). We prove the inversion theorem for the novel definition, and show that it shares the good properties of the usual definition.
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Fulvio Sbisà (2025) studied this question.
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