| 李建林.关于Strichartz的一个谱对准则[J].数学年刊A辑,2013,34(1):1~12 |
| 关于Strichartz的一个谱对准则 |
| On a Criterion of Strichartz for Spectral Pairs |
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| DOI： |
| 中文关键词: 迭代函数系, 自仿测度, 谱对, 和谐对 |
| 英文关键词:Iterated function system, Self-affine measure,Spectral pair, Compatible pair |
| 基金项目:国家自然科学基金 (No.11171201);中央高校基本科研业务费专项基金(No.GK201001002) |
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| 中文摘要: |
| 研究了与压缩迭代函数系和扩张迭代函数系相关的自仿测度的谱性质.在和谐对的条件下, 分别确定了谱对形成的一些充分条件和必要条件. 首先,给出了Strichartz谱对准则的几个等价形式. 其次,得到了这个谱对成立的两个必要条件. 最后,提供了Strichartz谱对准则的一个严格而详细的证明. |
| 英文摘要: |
| The author considers the spectrality of self-affine measures associated with a contractive iterated function system and an expansive iterated function system. Under the condition of a compatible pair, some necessary and sufficient conditions are determined respectively for a given pair to be a spectral pair.First, several equivalent forms of a criterion of Strichartz for spectral pairs are obtained.Then,two necessary conditions for the same spectral pair are obtained. Finally,a detailed and rigorous proof of this criterion is provided. |
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