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On a class of fractals: the constructive structure |
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| Authors: | SP Zhou GL He TF Xie |
| Institution: | a Faculty of Science, Zhejiang Institute of Science and Technology, Hangzhou, Zhejiang 310018, China b Institute of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, China c Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China d China Institute of Metrology, Hangzhou, Zhejiang 310034, China |
| Abstract: | In the present paper, we consider the following generalization of Besicovitch functions. Let {λn} satisfy Hadamard condition, write f(t)=∑∞n=1ancosλnt. We are interested in the intrinsic relationship among the coefficients {an}, the modulus of continuity of f and the upper Box dimension of graph of f. Especially, constructive structure of the function f which can be deduced from the (upper) Box dimension is a very interesting subject, and is hardly ever touched upon as far as we are aware. |
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