On the characterization of the dyadic derivative (Q1083642)

ALthough dyadic (Walsh) differentiation - see e.g. \textit{P. L. Butzer} and \textit{H. J. Wagner} [Appl. Anal. 3, 29-46 (1973; Zbl 0256.42016)] for a definition - has found wide interest in analysis and applications, the class of dyadic differentiable functions has up to now not been completely specified. In the present paper a general characterization theorem is proved which includes a result of \textit{V. A. Skvorcov} and \textit{W. R. Wade} [Anal. Math. 5, 249-255 (1979; Zbl 0429.42011)] as a special case. The latter stated that a continuous function which is dyadic differentiable except on a countable set of points is necessarily a constant. The author gives a good insight into the problems arising in characterizing classes of dyadic differentiable functions, he presents a couple of interesting examples and more than thirty references.