info:eu-repo/semantics/article
Absolute continuity of non-homogeneous self-similar measures
Fecha
2018-09Registro en:
Saglietti, Santiago Juan; Shmerkin, Pablo Sebastian; Solomyak, Boris; Absolute continuity of non-homogeneous self-similar measures; Academic Press Inc Elsevier Science; Advances in Mathematics; 335; 9-2018; 60-110
0001-8708
CONICET Digital
CONICET
Autor
Saglietti, Santiago Juan
Shmerkin, Pablo Sebastian
Solomyak, Boris
Resumen
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.