Proceedings of the American Mathematical Society

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

Author(s): Mats Anders Olofsson
Journal: Proc. Amer. Math. Soc. 129 (2001), 515-524.
MSC (2000): Primary 43A10; Secondary 26E10
Posted: August 28, 2000
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 43A10, 26E10

Mats Anders Olofsson
Affiliation: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden
Email: anderso@matematik.su.se

DOI: 10.1090/S0002-9939-00-05608-2
PII: S 0002-9939(00)05608-2
Keywords: Measure algebras, Wiener-Pitt phenomenon, independent powers
Received by editor(s): April 29, 1999
Posted: August 28, 2000
Additional Notes: The author was supported by the G. S. Magnusson Fund of the Royal Swedish Academy of Sciences
Communicated by: Christopher D. Sogge
Copyright of article: Copyright 2000, American Mathematical Society

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