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Decay of Walsh series and dyadic differentiation. (English) Zbl 0516.42032


MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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[1] P. L. Butzer and H. J. Wagner, Walsh-Fourier series and the concept of a derivative, Applicable Anal. 3 (1973), 29 – 46. Collection of articles dedicated to Eberhard Hopf on the occasion of his 70th birthday. · Zbl 0256.42016 · doi:10.1080/00036817308839055
[2] P. L. Butzer and H. J. Wagner, On dyadic analysis based on the pointwise dyadic derivative, Anal. Math. 1 (1975), no. 3, 171 – 196 (English, with Russian summary). · Zbl 0324.42011 · doi:10.1007/BF01930964
[3] N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372 – 414. · Zbl 0036.03604
[4] Adriano M. Garsia, Martingale inequalities: Seminar notes on recent progress, W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1973. Mathematics Lecture Notes Series. · Zbl 0284.60046
[5] N. R. Ladhawala, Absolute summability of Walsh-Fourier series, Pacific J. Math. 65 (1976), no. 1, 103 – 108. · Zbl 0318.42023
[6] J. Marcinkiewicz, Sur les multiplicateurs des séries de Fourier, Studia Math. 8 (1939), 79-91. · JFM 65.0257.02
[7] R. E. A. C. Paley, A remarcable series of orthogonal functions. I, Proc. London Math. Soc. 34 (1931), 241-264. · Zbl 0005.24806
[8] Gen-Ichirô Sunouchi, On the Walsh-Kaczmarz series, Proc. Amer. Math. Soc. 2 (1951), 5 – 11. · Zbl 0044.07103
[9] A. Zygmund, On the convergence and summability of power series in the circle of convergence. I, Fund. Math. 30 (1938), 170-196. · JFM 64.1054.01
[10] -, Trigonometric series, Vol. I, Cambridge Univ. Press, Cambridge, 1959.
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