Geodesic
Term by Term Dyadic Differentiation
Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 247-256

Voir la notice de l'article provenant de la source Cambridge University Press

Let ψ 0, ψ 1, ... denote the Walsh-Paley functions and let ∔ denote the group operation which Fine [5] defined on the interval [0, 1). Thus, if k ≧ 0 is an integer and if u, t are points in the interval [0, 1) then (where αk = 0 or 1 represents the kth coefficient of the binary expansion of t), and A real-valued function ƒ, is said to be dyadically differentiable at a point x ∈ [0, 1) if ƒ is defined at x and at x ∔ 2–n–1, n = 0, 1, ...;, and if the sequence (1) converges as N → ∞. 
Powell, Charles H.; Wade, William R. Term by Term Dyadic Differentiation. Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 247-256. doi: 10.4153/CJM-1981-020-2
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[1] 1. Butzer, P. L. and Wagner, H. J., Walsh-Fourier series and the concept of a derivative, Applicable Anal. 3 (1973), 29–46. Google Scholar

[2] 2. Butzer, P. L. and Wagner, H. J., On dyadic analysis based on the pointwise dyadic derivative, Analysis Math. 1 (1975), 171–196. Google Scholar

[3] 3. Coury, J. E., Walsh series with coefficients tending monotonically to zero, Pacific J. Math. 54 (1974), 1–16. Google Scholar

[4] 4. Coury, J. E., On the Walsh-Fourier coefficients of certain classes of functions, to appear. Google Scholar

[5] 5. Fine, N. J., On the Walsh Functions, Trans. Amer. Math. Soc. 65 (1949), 372–414. Google Scholar

[6] 6. Morgenthaler, G. W., On Walsh-Fourier series, Trans. Amer. Math. Soc. 84 (1957), 472–507. Google Scholar

[7] 7. Schipp, F., On term by term dyadic differentiation of Walsh series, Analysis Math. 2 (1976), 149–154. Google Scholar

[8] 8. Sölin, P., An inequality of Paley and convergence a.e. of Walsh-Fourier series, Ark. fur Mat. 7 (1969), 551–570. Google Scholar

[9] 9. Steckin, S. and Ul'janov, P. L., On sets of uniqueness, Izv. Akad. Nauk SSSR, Ser. Mat. 26 (1962), 211–222. Google Scholar

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