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APPROXIMATION WITH FRACTAL FUNCTIONS BY FRACTAL DIMENSION
Fractals ( IF 4.7 ) Pub Date : 2022-07-28 , DOI: 10.1142/s0218348x22501511
Y. S. LIANG 1
Affiliation  

On the basis of previous studies, we explore the approximation of continuous functions with fractal structure. We first give the calculation of fractal dimension of the linear combination of continuous functions with different Hausdorff dimension. Fractal dimension estimation of the linear combination of continuous functions with the same Hausdorff dimension has also been discussed elementary. Then, based on Weierstrass Theorem and the related results of Weierstrass function, we give the conclusion that the linear combination of polynomials with the same Hausdorff dimension approximates the objective function. The corresponding results with noninteger and integer Hausdorff dimensions have been investigated. We also give the preliminary applications of the theory in the last section.



中文翻译:

用分形维数逼近分形函数

在前人研究的基础上,我们探索了具有分形结构的连续函数的逼近。我们首先给出不同Hausdorff维数的连续函数线性组合的分形维数计算。对具有相同 Hausdorff 维数的连续函数的线性组合的分形维数估计也进行了初步讨论。然后,基于Weierstrass定理和Weierstrass函数的相关结果,我们得出具有相同Hausdorff维数的多项式的线性组合近似于目标函数的结论。已经研究了具有非整数和整数 Hausdorff 维数的相应结果。我们还在最后一节给出了该理论的初步应用。

更新日期:2022-07-28
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