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.
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Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 616-624 https://doi.org/10.4213/mzm12868.
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Skvortsov, V.A. Reconstruction of a Generalized Fourier Series from Its Sum on a Compact Zero-Dimensional Group in the Non-Abelian Case. Math Notes 109, 630–637 (2021). https://doi.org/10.1134/S0001434621030330
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DOI: https://doi.org/10.1134/S0001434621030330