Abstract:
It is proved that there exists a continuous function defined on [0,1]k2 whose double Fourier–Walsh–Paley series diverges almost everywhere in the sense of Pringsheim.
Bibliography: 9 titles
Citation:
R. D. Getsadze, “A continuous function with multiple Fourier series in the Walsh–Paley system that diverges almost everywhere”, Math. USSR-Sb., 56:1 (1987), 262–278
\Bibitem{Get85}
\by R.~D.~Getsadze
\paper A~continuous function with multiple Fourier series in the Walsh--Paley system that diverges almost everywhere
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 1
\pages 262--278
\mathnet{http://mi.mathnet.ru/eng/sm2127}
\crossref{https://doi.org/10.1070/SM1987v056n01ABEH003035}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=809489}
\zmath{https://zbmath.org/?q=an:0606.42026}
Linking options:
https://www.mathnet.ru/eng/sm2127
https://doi.org/10.1070/SM1987v056n01ABEH003035
https://www.mathnet.ru/eng/sm/v170/i2/p269
This publication is cited in the following 6 articles:
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
S. K. Bloshanskaya, I. L. Bloshanskii, “A weak generalized localization criterion for multiple Walsh–Fourier series with $J_k$-lacunary sequence of rectangular partial sums”, Proc. Steklov Inst. Math., 285 (2014), 34–55
G. A. Karagulyan, K. R. Muradyan, “On the divergence of Walsh and Haar series by sectorial and triangular regions”, Uch. zapiski EGU, ser. Fizika i Matematika, 2014, no. 2, 3–12
Bloshanskaya S.K., Bloshanskii I.L., “Local smoothness conditions on a function which guarantee convergence of double Walsh-Fourier series of this function”, Wavelet Analysis and Applications, Applied and Numerical Harmonic Analysis, 2007, 3–11
S. K. Bloshanskaya, I. L. Bloshanskii, T. Yu. Roslova, “Generalized localization for the double trigonometric Fourier series and the Walsh–Fourier series of functions in $L\log^+L\log^+\log^+L$”, Sb. Math., 189:5 (1998), 657–682
S. K. Bloshanskaya, I. L. Bloshanskii, “Generalized localization for the multiple Walsh–Fourier series of functions in $L_p$, $p\geqslant 1$”, Sb. Math., 186:2 (1995), 181–196
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