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Calculus on cantor triadic set (I)—derivative

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Abstract

For real-valued functions defined on Cantor triadic set, a derivative with corresponding formula of Newton-Leibniz’s type is given. In particular, for the self-similar functions and alternately jumping functions defined in this paper, their derivative and exceptional sets are studied accurately by using ergodic theory on Σ2 and Duffin-Schaeffer’s theorem concerning metric diophantine approximation. In addition, Haar basis of L2 (Σ2) is constructed and Haar expansion of standard self-similar function is given.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, 310027, Hangzhou

    Xl Llfeng

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  1. Xl Llfeng
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Supported by the Natural Science Foundation of Zhejiang Province.

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Llfeng, X. Calculus on cantor triadic set (I)—derivative. Appl. Math. Chin. Univ. 12, 483–492 (1997). https://doi.org/10.1007/s11766-997-0051-6

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  • DOI: https://doi.org/10.1007/s11766-997-0051-6

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