Polynomial approximation of self-similar measures and the spectrum of the transfer operator

Christoph Bandt; Helena Peña

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arXiv · 1512.02049

Polynomial approximation of self-similar measures and the spectrum of the transfer operator

Christoph Bandt·Helena Peña

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Abstract

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.

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Christoph Bandt, Helena Peña. 2016-05-12. Polynomial approximation of self-similar measures and the spectrum of the transfer operator. https://arxiv.org/abs/1512.02049

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