Abstract:
Trigonometric series summable by the Riemann method almost everywhere are considered. In particular, it is proved that if a multiple trigonometric series sums almost everywhere by the Riemann method to an integrable function f(x), and the Riemann majorant of this series satisfies a certain necessary condition, then the series is the Fourier series of the function f(x).
\Bibitem{Gev93}
\by G.~G.~Gevorkyan
\paper On uniqueness of multiple trigonometric series
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 80
\issue 2
\pages 335--365
\mathnet{http://mi.mathnet.ru/eng/sm1027}
\crossref{https://doi.org/10.1070/SM1995v080n02ABEH003528}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1251003}
\zmath{https://zbmath.org/?q=an:0828.42008}
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Linking options:
https://www.mathnet.ru/eng/sm1027
https://doi.org/10.1070/SM1995v080n02ABEH003528
https://www.mathnet.ru/eng/sm/v184/i11/p93
This publication is cited in the following 9 articles:
G. G. Gevorkyan, “Uniqueness theorems for simple trigonometric series with application to multiple series”, Sb. Math., 212:12 (2021), 1675–1693
G. G. Gevorkyan, “Uniqueness of Trigonometric Series”, J. Contemp. Mathemat. Anal., 55:6 (2020), 365
G. G. Gevorkyan, K. A. Navasardyan, “Uniqueness Theorems for Generalized Haar Systems”, Math. Notes, 104:1 (2018), 10–21
Mamikon Ginovyan, Karen Keryan, “Reconstruction of martingales and applications to multiple Haar series”, Studia Scientiarum Mathematicarum Hungarica, 55:4 (2018), 542
K. A. Kerian, “Uniqueness Theorem for Additive Functions and Its Applications to Orthogonal Series”, Math. Notes, 97:3 (2015), 362–375
L. D. Gogoladze, “On the problem of reconstructing the coefficients of convergent multiple function series”, Izv. Math., 72:2 (2008), 283–290
Citation in format AMSBIB
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