On a generalization of the concept of derivative. (English) Zbl 0345.42011


42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
43A55 Summability methods on groups, semigroups, etc.
43A75 Harmonic analysis on specific compact groups
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
Full Text: DOI


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[2] J. E. Gibbs, Some generalizations of the logical derivative,NPL, DES Rept.,8 (1971).
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[4] F. Schipp, Über einen Ableitungsbegriff von P. L. Butzer und H. J. Wagner,Matematica Balkanica,4 (1974), 541–546.
[5] P. Simon, Verallgemeinernten Walsh–Fourierreihen. II,Acta Math. Acad. Sci. Hungar. 27 (1976), 329–341. · Zbl 0335.42009 · doi:10.1007/BF01902112
[6] N. J. Vilenkin, On a class of complete orthonormal systems,Izv. Akad. Nauk SSSR, Ser. Math.,11 (1947), 363–400. · Zbl 0036.35601
[7] H. J. Wagner, Ein Differential-und Integralkalkül in der Walsh-Fourier-Analysis mit Anwendungen (Forschungber. des Landes Nordhein-Westfalen Nr 2334), Westdeutscher Verlag (Köln-Opladen, 1973), 71 pp.
[8] A. Zygmund,Trigonometric series (Cambridge, 1959). · Zbl 0085.05601
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