Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures
Volume 117 / 1995
Studia Mathematica 117 (1995), 1-28
DOI: 10.4064/sm-117-1-1-28
Abstract
The Choquet-Deny theorem and Deny's theorem are extended to the vector-valued case. They are applied to give a simple nonprobabilistic proof of the vector-valued renewal theorem, which is used to study the $L^p$-dimension, the $L^p$-density and the Fourier transformation of vector-valued self-similar measures. The results answer some questions raised by Strichartz.
