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. 
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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/

[1] V. A. Skvortsov, F. Tulone, “Kurzweil–Henstock type integral on zero-dimensional group and some of its applications”, Czechoslovak Math. J., 58:4 (2008), 1167–1183 | DOI | MR | Zbl

[2] V. A. Skvortsov, F. Tulone, “Henstock–Kurzweil type integral in Fourier analysis on zero-dimensional group”, Tatra Mt. Math. Publ., 44 (2009), 41–51 | DOI | MR | Zbl

[3] A. Bokkuto, V. A. Skvortsov, F. Tulone, “Integrirovanie funktsii so znacheniyami v kompleksnom prostranstve Rissa i nekotorye prilozheniya v garmonicheskom analize”, Matem. zametki, 98:1 (2015), 12–26 | DOI | MR

[4] E. Khyuitt, K. Ross, Abstraktnyi garmonicheskii analiz. T. 1. Struktura topologicheskikh grupp. Teoriya integrirovaniya. Predstavleniya grupp, Nauka, M., 1975 | MR | Zbl

[5] E. B. Vinberg, Lineinye predstavleniya grupp, Nauka, M., 1985 | MR

[6] M. A. Naimark, Teoriya predstavlenii grupp, Nauka, M., 1976 | MR

[7] G. N. Agaev, N. Ya. Vilenkin, G. M. Dzhafarli, A. I Rubinshtein, Multiplikativnye sistemy funktsii i garmonicheskii analiz na nul-mernykh gruppakh, Elm, Baku, 1981 | MR

[8] D. J. Grubb, “Sets of uniqueness in compact, 0-dimensional metric groups”, Trans. Amer. Math. Soc., 301 (1987), 239–249 | MR | Zbl

[9] B. S. Thomson, “Derivation bases on the real line. I”, Real Anal. Exchange, 8:1 (1982), 67–207 | DOI | MR

[10] V. A. Skvortsov, F. Tulone, “Ob integrale perronovskogo tipa na kompaktnoi nul-mernoi abelevoi gruppe”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2008, no. 3, 37–42 | MR | Zbl

[11] T. P. Lukashenko, V. A. Skvortsov, A. P. Solodov, Obobschennye integraly, URSS, M., 2011