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

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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.
Opis fizyczny
  • Department Of Mathematics, University Of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
  • Houston Advanced Research Center, 4800 Research Forest Drive, The Woodlands, Texas 77381, U.S.A.
  • Goldsmiths' College, University Of London, London Se14, England
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