| CALCULUS ON CANTOR TRIADIC SET （I）——DERIVATIVE |
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| 作者姓名： | XiLIFENG |
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| 作者单位： | DepartmentofMathematics,ZhejiangUniversity,Hangzhou310027 |
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| 摘 要： | For real-valued functions defined on Cantor triadic ,set. a derivative with corresponding formula of Newton-Leihniz‘s type is given In particular, for the self-simltar functions and alter-nately jumping functions defined in this paper, their derivative and exceptional sets are studied ac-curately by using ergodic theory on Е2 and Duffin-Scbaeffer‘s theorem coneerning metric diophan-tine approximation. In addition, Haar basis of L2(Е2) is constructed and Flaar expansion of stan-drd self-similar function is given.
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| 关 键 词： | 微积分学 CANTOR三元集 导数 真值函数 |
| 收稿时间： | 14 June 1995 |
Calculus on cantor triadic set (I)—derivative |
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| XiLIFENG.Calculus on cantor triadic set (I)—derivative[J].Applied Mathematics A Journal of Chinese Universities,1997,12(4):483-492. |
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| Authors: | Xl Llfeng |
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| Institution: | (1) Department of Mathematics, Zhejiang University, 310027, Hangzhou |
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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.
Supported by the Natural Science Foundation of Zhejiang Province. |
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| Keywords: | Fractal derivative on Cantor set exceptional set ergodic theory Duffin-Schaeffer’ s theorem |
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