Abstract
We construct finitely supported symmetric probability measures on \(S{L}_{2}(\mathbb{R})\) for which the Furstenberg measure on \({\mathbb{P}}_{1}(\mathbb{R})\) has a smooth density.
Keywords
- Probability Measure
- Haar Measure
- Projective Action
- Absolute Continuity
- Similar Construction
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Acknowledgements
The author is grateful to C. McMullen and P. Varju for several related discussions. Research was partially supported by NSF grants DMS-0808042 and DMS-0835373
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© 2012 Springer-Verlag Berlin Heidelberg
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Bourgain, J. (2012). Finitely Supported Measures on \(S{L}_{2}(\mathbb{R})\) Which are Absolutely Continuous at Infinity. In: Klartag, B., Mendelson, S., Milman, V. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29849-3_7
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DOI: https://doi.org/10.1007/978-3-642-29849-3_7
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-642-29849-3
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