Abstract:
We construct an integrable function whose Fourier series possesses the following property. After an appropriate
choice of signs of the coefficients of this series, the partial sums of the resulting series are dense in Lp, p∈(0,1).
\Bibitem{GriGal21}
\by M.~G.~Grigoryan, L.~N.~Galoyan
\paper Functions universal with respect to the trigonometric system
\jour Izv. Math.
\yr 2021
\vol 85
\issue 2
\pages 241--261
\mathnet{http://mi.mathnet.ru/eng/im8964}
\crossref{https://doi.org/10.1070/IM8964}
\zmath{https://zbmath.org/?q=an:1464.42003}
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https://www.mathnet.ru/eng/im8964
https://doi.org/10.1070/IM8964
https://www.mathnet.ru/eng/im/v85/i2/p73
This publication is cited in the following 8 articles:
L. N. Galoyan, M. G. Grigoryan, “Functions Almost Universal in the Sense of Signs with Respect to the Trigonometric System and the Walsh System”, Math. Notes, 115:6 (2024), 1030–1034
M. G. Grigoryan, “On universal (in the sense of signs) Fourier series with respect to the Walsh system”, Sb. Math., 215:6 (2024), 717–742
M. G. Grigoryan, S. V. Konyagin, “On Fourier series in the multiple trigonometric system”, Russian Math. Surveys, 78:4 (2023), 782–784
S. A. Sargsyan, L. N. Galoyan, “On the uniform convergence of spherical partial sums of Fourier series by the double Walsh system”, J. Contemp. Mathemat. Anal., 58:5 (2023), 370
M. G. Grigoryan, A. A. Sargsyan, “On the existence and structure of universal functions for weighted spaces L1μ[0,1]”, J. Math. Sci., 271:5 (2023), 644
M. G. Grigoryan, “On universal Fourier series in the Walsh system”, Siberian Math. J., 63:5 (2022), 868–882
M. G. Grigoryan, “On Almost Universal Double Fourier Series”, Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S129–S139
M. G. Grigoryan, “On Fourier series almost universal in the class of measurable functions”, J. Contemp. Mathemat. Anal., 57:4 (2022), 215–221
Citation in format AMSBIB
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