Geodesic
Reconstruction of a Generalized Fourier Series from Its Sum on a Compact Zero-Dimensional Group in the Non-Abelian Case
Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 616-624

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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. 
@article{MZM_2021_109_4_a12,
     author = {V. A. Skvortsov},
     title = {Reconstruction of a {Generalized} {Fourier} {Series} from {Its} {Sum} on a {Compact} {Zero-Dimensional} {Group} in the {Non-Abelian} {Case}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {616--624},
     publisher = {mathdoc},
     volume = {109},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a12/}
}
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V. A. Skvortsov. Reconstruction of a Generalized Fourier Series from Its Sum on a Compact Zero-Dimensional Group in the Non-Abelian Case. Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 616-624. http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a12/