Absolutely continuous measures on non quasi-analytic curves with independent powers

Olofsson, Mats

doi:10.1090/S0002-9939-00-05608-2

Absolutely continuous measures on non quasi-analytic curves with independent powers
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by Mats Anders Olofsson PDF

Proc. Amer. Math. Soc. 129 (2001), 515-524 Request permission

Abstract:

We prove that every non quasi-analytic Carleman class contains functions whose graph supports measures that are absolutely continuous with respect to arc length measure and yet they have independent convolution powers in the measure algebra $M(\mathbb {R}^2)$. The proof relies on conditions which ensure that the canonical map between two Cantor sets can be extended to a function in an arbitrary prescribed non quasi-analytic Carleman class.

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