Polynomial approximation of self-similar measures and the spectrum of the transfer operator
Polynomial approximation of self-similar measures and the spectrum of the transfer operator
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DOI：
10.3934/dcds.2017198
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发表时间：
2015-12
期刊：
影响因子：
--
通讯作者：
C. Bandt;Helena Pena
中科院分区：
文献类型：
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作者：
C. Bandt;Helena Pena
我们考虑$\mathbb R.$上的自相似测度哈钦森算子H作用于测度，是作用于连续函数的转移算子T的对偶。我们确定多项式特征函数的$T。$因此，我们得到的特征值$H$和自然多项式近似的自相似措施。作为一个例子，伯努利卷积进行了研究。
We consider self-similar measures on $\mathbb R.$ The Hutchinson operator $H$ acts on measures and is the dual of the transfer operator $T$ which acts on continuous functions. We determine polynomial eigenfunctions of $T .$ As a consequence, we obtain eigenvalues of $H$ and natural polynomial approximations of the self-similar measure. Bernoulli convolutions are studied as an example.