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

الأصل · EN

We consider self-similar measures on 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.