Abstract:
For simple trigonometric series it is shown, in particular, that if the trigonometric series is Riemann summable in measure to an integrable function f and if the Riemann majorant is finite everywhere except possibly on a countable set, then this series is the Fourier series of the function f. Uniqueness theorems for multiple trigonometric series are obtained on the basis of this result.
Bibliography: 14 titles.
Citation:
G. G. Gevorkyan, “Uniqueness theorems for simple trigonometric series with application to multiple series”, Sb. Math., 212:12 (2021), 1675–1693
\Bibitem{Gev21}
\by G.~G.~Gevorkyan
\paper Uniqueness theorems for simple trigonometric series with application to multiple series
\jour Sb. Math.
\yr 2021
\vol 212
\issue 12
\pages 1675--1693
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\crossref{https://doi.org/10.1070/SM9525}
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Linking options:
https://www.mathnet.ru/eng/sm9525
https://doi.org/10.1070/SM9525
https://www.mathnet.ru/eng/sm/v212/i12/p20
This publication is cited in the following 4 articles:
G. G. Gevorkyan, “On uniqueness for series in the general Franklin system”, Sb. Math., 215:3 (2024), 308–322
G. G. Gevorkyan, “On uniqueness for Franklin series with a convergent subsequence of partial sums”, Sb. Math., 214:2 (2023), 197–209
G. G. Gevorkyan, V. G. Mikaelyan, “Uniqueness of series by general Franklin system with convergent subsequence of partial sums”, J. Contemp. Mathemat. Anal., 58:2 (2023), 67
M. G. Plotnikov, “Uniqueness sets of positive measure for the trigonometric system”, Izv. Math., 86:6 (2022), 1179–1203
Citation in format AMSBIB
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