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Convolution in perfect Lie groups
| Content Provider | Scilit |
|---|---|
| Author | Benoist, Yves Saxcé, Nicolas D. E. |
| Copyright Year | 2016 |
| Description | LetGbe a connected perfect real Lie group. We show that there exists α < dimGandp∈ $\mathbb{N}$ * such that if μ is a compactly supported α-Frostman Borel measure onG, then thepth convolution power $μ*^{p}$is absolutely continuous with respect to the Haar measure onG, with arbitrarily smooth density. As an application, we obtain that ifA⊂Gis a Borel set with Hausdorff dimension at least α, then thep-fold product $setA^{p}$contains a non-empty open set. |
| Related Links | http://pdfs.semanticscholar.org/7c31/b4c3ae2f0d6a381b93a1bca39879bbaf3767.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A341A4339431AAF6C6DFAAAFF0441AF6/S0305004116000074a.pdf/div-class-title-convolution-in-perfect-lie-groups-div.pdf |
| Ending Page | 45 |
| Page Count | 15 |
| Starting Page | 31 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004116000074 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 1 |
| Volume Number | 161 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2016-07-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
