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We analyze the Fourier transform of vector measures $$\nu $$ ν as well as the convolution between scalar and vector-valued regular measures defined on the Borel sets of a compact abelian group. We make special emphasis on the Riemann–Lebesgue lemma and Young’s convolution type results in this setting. Applications to Fourier transform and convolutions between functions in $$L^p(\nu )$$...
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