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| The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES |
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Citation： |
Ren Fuyao,Liang Jinrong.The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES[J].Chinese Annals of Mathematics B,1995,16(2):153~162 |
| Page view： 1099
Net amount： 654 |
Authors： |
Ren Fuyao; Liang Jinrong |
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| Abstract： |
This paper studies the Hausdorff dimensions, the Hausdorff measures of generalized Moran fractals and the convergence of the Fourier series of functions defined on some generalized Moran fractals.A general formula is given for the calculation of the Hausdorff dimensions of generalized Moran fractals and it is proved that their Hausdorff measures are finite positive numbers under some conditions. In addition, the authors define an orthonormal system $ \Phi $ of functions defined on generalized Moran$s$-sets $(gMs)$ and discuss the convergence of the Fourier series,with respect to $ \Phi $, of each function $ f(x)\in L^1(gMs,H^s) $. |
Keywords： |
Haudorff dimension, Hausdorff measure, $s$-set,Differentiation base,Fourier series. |
Classification： |
28A78 |
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