A+ CATEGORY SCIENTIFIC UNIT

Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures

Volume 117 / 1995

Ka-Sing Lau 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.

Authors

  • Ka-Sing Lau

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