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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 1, Pages 41–60 (Mi izv227)  

This article is cited in 18 scientific papers (total in 18 papers)

On Walsh series with monotone coefficients

G. G. Gevorkyana, K. A. Navasardyanb

a Institute of Mathematics, National Academy of Sciences of Armenia
b Yerevan State University

Abstract: We prove that if $a_n\downarrow 0$ and $\sum_{n=0}^\infty a_n^2=+\infty$ then the Walsh series $\sum_{n=0}^\infty a_nW_n(x)$ has the following property. For any measurable function $f(x)$ which is finite almost everywhere, there are numbers $\delta_n=0,\pm 1$ such that the series $\sum_{n=0}^\infty\delta_na_nW_n(x)$ converges to $f(x)$ almost everywhere. This assertion complements and strengthens previously known results about universal Walsh series and Walsh null-series.

DOI: https://doi.org/10.4213/im227

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English version:
Izvestiya: Mathematics, 1999, 63:1, 37–55

Bibliographic databases:

MSC: 42C10
Received: 30.09.1997

Citation: G. G. Gevorkyan, K. A. Navasardyan, “On Walsh series with monotone coefficients”, Izv. RAN. Ser. Mat., 63:1 (1999), 41–60; Izv. Math., 63:1 (1999), 37–55

Citation in format AMSBIB
\by G.~G.~Gevorkyan, K.~A.~Navasardyan
\paper On Walsh series with monotone coefficients
\jour Izv. RAN. Ser. Mat.
\yr 1999
\vol 63
\issue 1
\pages 41--60
\jour Izv. Math.
\yr 1999
\vol 63
\issue 1
\pages 37--55

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    This publication is cited in the following articles:
    1. Sargsyan A., Grigoryan M., “Universal Functions With Respect to the Double Walsh System For Classes of Integrable Functions”, Anal. Math.  crossref  isi
    2. Grigoryan M.G., “Functions, Universal With Respect to the Classical Systems”, Adv. Oper. Theory  crossref  isi
    3. R. G. Melikbekyan, “On quasi-universal Walsh series in $L^p_{[0,1]}$, $p\in[1,2]$”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 1, 22–29  mathnet
    4. L. N. Galoyan, R. G. Melikbekyan, “Behavior of the Fourier–Walsh coefficients of a corrected function”, Siberian Math. J., 57:3 (2016), 505–512  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. M. G. Grigoryan, A. A. Sargsyan, “On existence of a universal function for $L^p[0,1]$ with $p\in(0,1)$”, Siberian Math. J., 57:5 (2016), 796–808  mathnet  crossref  crossref  isi  elib
    6. Grigoryan M.G., Sargsyan A.A., “On the universal function for the class L p [0,1], p (0,1)”, J. Funct. Anal., 270:8 (2016), 3111–3133  crossref  mathscinet  zmath  isi  elib  scopus
    7. Grigoryan M.G., Navasardyan K.A., “On behavior of Fourier coefficients by Walsh system”, J. Contemp. Math. Anal.-Armen. Aca., 51:1 (2016), 21–33  crossref  mathscinet  zmath  isi  scopus
    8. Sargsyan A., Grigoryan M., “Universal Function For a Weighted Space l-Mu(1) [0,1]”, Positivity, 21:4 (2017), 1457–1482  crossref  mathscinet  zmath  isi  scopus
    9. M. G. Grigoryan, A. A. Sargsyan, “The structure of universal functions for $L^p$-spaces, $p\in(0,1)$”, Sb. Math., 209:1 (2018), 35–55  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. Grigoryan M., Grigoryan T., Sargsyan A., “On the Universal Function For Weighted Spaces l-Mu(P)[0,1], P >= 1”, Banach J. Math. Anal., 12:1 (2018), 104–125  crossref  mathscinet  zmath  isi
    11. A. A. Sargsyan, “Quasiuniversal Fourier–Walsh Series for the Classes $L^p[0,1]$, $p>1$”, Math. Notes, 104:2 (2018), 278–292  mathnet  crossref  crossref  mathscinet  isi  elib
    12. Sargsyan A., Grigoryan M., “Universal Functions For Classes l-P[0,1)2, P Is An Element of(0,1), With Respect to the Double Walsh System”, Positivity, 23:5 (2019), 1261–1280  crossref  isi
    13. Grigoryan M., Sargsyan A., “On the Structure of Universal Functions For Classes l-P[0,1)(2), P Is An Element of (0,1), With Respect to the Double Walsh System”, Banach J. Math. Anal., 13:3 (2019), 647–674  crossref  isi
    14. Sargsyan A.A., “On the Structure of Functions, Universal For Weighted Spaces”, J. Contemp. Math. Anal.-Armen. Aca., 54:3 (2019), 163–175  crossref  isi
    15. M. G. Grigoryan, “Functions with universal Fourier-Walsh series”, Sb. Math., 211:6 (2020), 850–874  mathnet  crossref  crossref  mathscinet  isi  elib
    16. Sargsyan A., “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  crossref  isi
    17. Grigoryan M.G., “Functions Universal With Respect to the Walsh System”, J. Contemp. Math. Anal.-Armen. Aca., 55:6 (2020), 376–388  crossref  isi
    18. M. G. Grigoryan, L. N. Galoyan, “Functions universal with respect to the trigonometric system”, Izv. Math., 85:2 (2021), 241–261  mathnet  crossref  crossref
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