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Kurzweil-Henstock integral; derivation basis; locally compact zero-dimensional abelian group; characters of a group; multiplicative integral transform; inversion formula.
A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.
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