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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1797134