| The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES |
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| 引用本文： | Ren Fuyao,Liang Jinrong. The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES[J]. 数学年刊B辑(英文版), 1995, 16(2): 153-162 |
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| 作者姓名： | Ren Fuyao Liang Jinrong |
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| 摘 要： | ＴｈｅＨＡＵＳＤＯＲＦＦＤＩＭＥＮＳＩＯＮＡＮＤＭＥＡＳＵＲＥＯＦＴＨＥＧＥＮＥＲＡＬＩＺＥＤＭＯＲＡＮＦＲＡＣＴＡＬＳＡＮＤＦＯＵＲＩＥＲＳＥＲＩＥＳ￥ＲＥＮＦＵＴｈＯ；ＬＩＡＮＧＪＩＮＲＯＮＧＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｓｔｕｄｉｅｓｔｈ...
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| 关 键 词： | 豪斯多夫维度 测度 基数分化 傅里叶序列 欧几里德空间 |
| 收稿时间： | 1993-07-08 |
The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES |
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| Ren Fuyao and Liang Jinrong. The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES[J]. Chinese Annals of Mathematics,Series B, 1995, 16(2): 153-162 |
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| Authors: | Ren Fuyao and Liang Jinrong |
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| Affiliation: | REN FUThO;LIANG JINRONG |
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| Abstract: | This paper studies the Hausdorff dimensions, the Hausdorff measures of generalized Moranfrontals and the convergence of the Fourier series of functions defined on some generalizedMoran fractals. A general formula is given for the calculatinn of the Hausdorff dimensions ofgeneralized Moran fractals and it is proved that their Hausdorff measures are finite positivenumbers under some conditions. In addition, the authors define an orthonormal system offunctions defilled on generalized Moran s-sets (gMs) and discuss the convergence of the Fourierseries, with respect to of each function f(x) E L1(gMs, Hs). |
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| Keywords: | Haudorff dimension Hausdorff measure s-set Differentiation base Fourier series. |
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