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

Ka-Sing LauJian-Rong WangCho-Ho Chu — 1995

Studia Mathematica

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.

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