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ArticleOriginal scientific text

Title

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

Authors 1, 2, 3

Affiliations

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

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 Lp-dimension, the Lp-density and the Fourier transformation of vector-valued self-similar measures. The results answer some questions raised by Strichartz.

Keywords

ENG
Choquet-Deny theorem, convolution, exponential function, matrices, renewal equation, self-similar measures

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Studia Mathematica
1995-1996/117/1
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Pages:
1-28
Main language of publication
English
Received
1994-01-25
Accepted
1995-05-31
Published
1995
Exact and natural sciences