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关于一些自仿测度的绝对连续性和奇异性 被引量：1

On absolute continuity and singularity of some self-affine measures
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摘要 奇异性是测度的一个重要性质,由定义得到某些自仿测度奇异的一个充分条件.借助于特征函数和测度的傅里叶变换,利用测度绝对连续性的定义,找到一类绝对连续的自仿测度,并对Li J-L的2个结论给出了简单的应用. Singularity is an important property of measures.A sufficient condition on singularity of some self-affine measures is obtained by using the definition.A class of absolutely continuous self-affine measure is found by using Fourier transform and the definition of measure′s absolute continuity.Some simple applications on two results of Li J-L are given.
作者 杜雅琴
机构地区 陕西师范大学数学与信息科学学院
出处 《纺织高校基础科学学报》 CAS 2011年第3期382-385,402,共5页 Basic Sciences Journal of Textile Universities
关键词 迭代函数系 自仿测度 奇异性 绝对连续性 Bernoulli卷积 iterated function systems self-affine measure singularity absolute continuity Bernoulli convolution
分类号 O174.12 [理学—基础数学]
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参考文献8

  • 1NIU M, XI L F. Singularity of a class of self-similar measures [ J ]. Chaos Solitons Fractals ,2007,34:376-382.
  • 2Li J L. Singularity of certain self-affine measures[ J]. J Math Anal Appl,2008 ,347 :375-380.
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同被引文献11

  • 1HUTCHINSON J E. Fractals and self-similarity[J]. Indiana Univ Math J, 1981,30,713-747.
  • 2JORGENSEN P E T, PEDERSEN S. Dense analytic subspaces in fractal L2-spaces[J]. J Anal Math, 1998,75 : 185-228.
  • 3FUGLEDE B. Commuting self-adjoint partial differential operators and a group theoretic problem[J]. J Funct Anal, 1974,16:101-121.
  • 4LI Jianlin. On the k,-orthogonal exponentials[J]. Nonlinear Analysis,2010,73:940-951.
  • 5DUTKAY D E, DUTKAY P E T. Jorgenseru Analysis of orthogonality and of orbits in affine iterated function systems [J]. Math Z,2007,256 :801-823.
  • 6LI Jianlin. Non-spectral problem for a class of planar self-affine measures[J]. J Funet Anal,2008,255:3 125-3 148.
  • 7LI Jianlin. Non-spectrality of planar self-affine measures with three-elements digit sctl-J3. J Funct Anal,2009,257: 537- 552.
  • 8LI Jianlin.μu,D-orthogonality and compatible pair[J]. J Funct Anal, 2007,224 .. 628-638.
  • 9张陇生.自仿测度的谱性质[J].纺织高校基础科学学报,2009,22(4):445-448. 被引量：3
  • 10王美莲.L^2空间中的非谱问题[J].纺织高校基础科学学报,2010,23(4):464-467. 被引量：3

引证文献1

纺织高校基础科学学报
2011年 第3期

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