Abstract:
The paper sheds light on the structure of functions which are universal for Lp-spaces, p∈(0,1), with respect to the signs of Fourier-Walsh coefficients. It is shown that there exists a measurable set E⊂[0,1], whose measure is arbitrarily close to 1, such that by an appropriate change of values of any function f∈L1[0,1] outside E a function ˜f∈L1[0,1] can be obtained that is universal for each Lp[0,1]-space, p∈(0,1), with respect to the signs of Fourier-Walsh coefficients.
Bibliography: 28 titles.
Keywords:
universal function, Fourier coefficients, Walsh system, convergence in a metric.
\Bibitem{GriSar18}
\by M.~G.~Grigoryan, A.~A.~Sargsyan
\paper The structure of universal functions for $L^p$-spaces, $p\in(0,1)$
\jour Sb. Math.
\yr 2018
\vol 209
\issue 1
\pages 35--55
\mathnet{http://mi.mathnet.ru/eng/sm8806}
\crossref{https://doi.org/10.1070/SM8806}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3740295}
\zmath{https://zbmath.org/?q=an:1392.42027}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2018SbMat.209...35G}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000428795800002}
\elib{https://elibrary.ru/item.asp?id=30762118}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045635016}
Linking options:
https://www.mathnet.ru/eng/sm8806
https://doi.org/10.1070/SM8806
https://www.mathnet.ru/eng/sm/v209/i1/p37
This publication is cited in the following 15 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, “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, L. N. Galoyan, “Functions universal with respect to the trigonometric system”, Izv. Math., 85:2 (2021), 241–261
M. G. Grigoryan, “Ob universalnykh ryadakh Fure—Uolsha”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 200, VINITI RAN, M., 2021, 45–57
M. G. Grigoryan, “On the existence and structure of universal functions”, Dokl. Math., 103:1 (2021), 23–25
M. G. Grigoryan, “Functions with universal Fourier-Walsh series”, Sb. Math., 211:6 (2020), 850–874
M. G. Grigoryan, “Universal Fourier Series”, Math. Notes, 108:2 (2020), 282–285
A. Sargsyan, “On the existence of universal functions with respect to the double walsh system for classes of integrable functions”, Colloq. Math., 161:1 (2020), 111–129
Sargsyan A., Grigoryan M., “Universal Functions With Respect to the Double Walsh System For Classes of Integrable Functions”, Anal. Math., 46:2 (2020), 367–392
Grigoryan M.G., “Functions, Universal With Respect to the Classical Systems”, Adv. Oper. Theory, 5:4 (2020), 1414–1433
M. G. Grigoryan, “Functions universal with respect to the walsh system”, J. Contemp. Math. Anal.-Armen. Aca., 55:6 (2020), 376–388
M. Grigoryan, A. Sargsyan, “On the structure of universal functions for classes Lp[0,1)2 , p∈(0,1) , with respect to the double Walsh system”, Banach J. Math. Anal., 13:3 (2019), 647–674
A. A. Sargsyan, “On the structure of functions universal for the weighted spaces Lpμ[0,1] , p>1”, J. Contemp. Math. Anal., 54:3 (2019), 163–175
M. Grigoryan, L. Galoyan, “On Fourier series that are universal modulo signs”, Studia Math., 249:2 (2019), 215–231
A. Sargsyan, M. Grigoryan, “Universal functions for classes Lp[0,1)2 , p∈(0,1) , with respect to the double Walsh system”, Positivity, 23:5 (2019), 1261–1280
Citation in format AMSBIB
Contact us: