×

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


MSC:

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
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] P. L. Butzer –H. J. Wagner, Walsh – Fourier series and the concept of a derivative,Applicable Anal.,3 (1973), 29–46. · Zbl 0256.42016 · doi:10.1080/00036817308839055
[2] J. E. Gibbs, Some generalizations of the logical derivative,NPL, DES Rept.,8 (1971).
[3] C. W. Onneweer, Differentiability for Rademacher series on groups,Acta Sci. Math. Szeged (to appear). · Zbl 0356.43007
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.