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


Author: Mats Anders Olofsson
Journal: Proc. Amer. Math. Soc. 129 (2001), 515-524
MSC (2000): Primary 43A10; Secondary 26E10
DOI: https://doi.org/10.1090/S0002-9939-00-05608-2
Published electronically: August 28, 2000
MathSciNet review: 1797134
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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.


References [Enhancements On Off] (What's this?)

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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-00-05608-2
Keywords: Measure algebras, Wiener-Pitt phenomenon, independent powers
Received by editor(s): April 29, 1999
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society

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