Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904624 | Advances in Mathematics | 2018 | 51 Pages |
Abstract
We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S.-M. Ngai and Y. Wang. While recently there has been much progress in understanding absolute continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case. In the course of the proof, we establish new results on the dimension and Fourier decay of a class of random self-similar measures.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Santiago Saglietti, Pablo Shmerkin, Boris Solomyak,