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Polynomial approximation of self-similar measures and the spectrum of the transfer operator
We consider self-similar measures on The Hutchinson operator
acts on measures and is the dual of the transfer operator which acts on
continuous functions. We determine polynomial eigenfunctions of As a
consequence, we obtain eigenvalues of and natural polynomial approximations
of the self-similar measure. Bernoulli convolutions are studied as an example.Comment: 15 pages, 8 figure