Abstract:
A necessary and sufficient condition for a formal series with respect to the system of irreducible representations of a compact zero-dimensional group to be the Fourier–Stieltjes series of an additive measure is found. It is shown that, in the case of pointwise convergence of such a series everywhere on the group, its sum is integrable in the sense of Henstock-type integral, and the given series is the Fourier–Henstock series of its sum.
Keywords:zero-dimensional compact groups, irreducible unitary representations of a group, additive complex measure, Fourier–Stieltjes operator coefficients, Henstock–Kurzweil integral on a group.
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