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| FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION | |
| 作者姓名： | ZhouSongping YaoKui SuWeiyi |
| 作者单位： | [1]ZhejiangSci-TechUniversity,China [2]NanjingUniversity,China |
| 摘 要： | The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions. |
| 关 键 词： | 魏尔斯特拉斯方程 流形几何 豪斯多夫维度 积分函数 |
| 收稿时间： | 18 February 2003 |
Fractional integrals of the Weierstrass functions: The exact box dimension |
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| ZhouSongping YaoKui SuWeiyi.Fractional integrals of the Weierstrass functions: The exact box dimension[J].Analysis in Theory and Applications,2004,20(4):332-341. | |
| Authors: | |
| Institution: | Zhou Songping Institute of Mathematics Zhejiang Institute of Sciences and TechnologyHangzhou 310018P. R. ChinaYao Kui and Su Weiyi Department of Mathematics Nanjing University Nanjing 210093 P. R. China |
| Abstract: | The present paper investigates the fractal structure of fractional integrals of Weierstrass functions.The exact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions. |
| Keywords: | fractal fractional calculus Weierstrass function box dimension FUNCTIONS INTEGRALS FRACTIONAL BOX DIMENSION general groups especially lower bounds novel ideas Hausdorff dimension new technique method result interesting need point exact box dimension cases |
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