Abstract:
We prove results on the existence of functions whose Fourier series in the Walsh system are universal in some sense or other
in the function classes Lp[0,1], 0<p<1, and M[0,1]. We also give a description of the structure of these functions.
Bibliography: 30 titles.
Keywords:
universal functions, Fourier-Walsh series, convergence, almost everywhere convergence.
This research was carried out with the financial support of the State Committee on Science of the Ministry of Education and Science of the Republic of Armenia (project no. 18T-1A148).
\Bibitem{Gri20}
\by M.~G.~Grigoryan
\paper Functions with universal Fourier-Walsh series
\jour Sb. Math.
\yr 2020
\vol 211
\issue 6
\pages 850--874
\mathnet{http://mi.mathnet.ru/eng/sm9302}
\crossref{https://doi.org/10.1070/SM9302}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4104777}
\zmath{https://zbmath.org/?q=an:1447.42031}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2020SbMat.211..850G}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000564137700001}
\elib{https://elibrary.ru/item.asp?id=45172678}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85094980669}
Linking options:
https://www.mathnet.ru/eng/sm9302
https://doi.org/10.1070/SM9302
https://www.mathnet.ru/eng/sm/v211/i6/p107
This publication is cited in the following 13 articles:
Sergo A. Episkoposian, Martin G. Grigorian, Tigran M. Grigorian, “On the universal pair with respect to the generalized Walsh system”, Adv. Oper. Theory, 9:1 (2024)
M. G. Grigoryan, T. M. Grigoryan, L. S. Simonyan, Trends in Mathematics, 3, Extended Abstracts 2021/2022, 2024, 117
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
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. Math. Anal., Armen. Acad. Sci., 57:4 (2022), 215–221
M. G. Grigoryan, “On unconditional and absolute convergence of the Haar series in the metric of Lp[0,1] with 0<p<1”, Siberian Math. J., 62:4 (2021), 607–615
M. G. Grigoryan, “On the existence and structure of universal functions”, Dokl. Math., 103:1 (2021), 23–25
M. G. Grigoryan, “Universal Fourier Series”, Math. Notes, 108:2 (2020), 282–285
M. G. Grigoryan, “Functions universal with respect to the Walsh system”, J. Contemp. Math. Anal., Armen. Acad. Sci., 55:6 (2020), 376–388
Citation in format AMSBIB
Contact us: