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

Ka-Sing Lau; Jian-Rong Wang; Cho-Ho Chu

Studia Mathematica (1995)

  • Volume: 117, Issue: 1, page 1-28
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Lau, Ka-Sing, Wang, Jian-Rong, and Chu, Cho-Ho. "Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures." Studia Mathematica 117.1 (1995): 1-28. <http://eudml.org/doc/216238>.

@article{Lau1995,
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.},
author = {Lau, Ka-Sing, Wang, Jian-Rong, Chu, Cho-Ho},
journal = {Studia Mathematica},
keywords = {Choquet-Deny theorem; convolution; exponential function; matrices; renewal equation; self-similar measures; -dimension; -density; locally compact abelian groups; vector-valued measures; convolution powers; Markov chains; theorem of Deny},
language = {eng},
number = {1},
pages = {1-28},
title = {Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures},
url = {http://eudml.org/doc/216238},
volume = {117},
year = {1995},
}

TY - JOUR
AU - Lau, Ka-Sing
AU - Wang, Jian-Rong
AU - Chu, Cho-Ho
TI - Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures
JO - Studia Mathematica
PY - 1995
VL - 117
IS - 1
SP - 1
EP - 28
AB - 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.
LA - eng
KW - Choquet-Deny theorem; convolution; exponential function; matrices; renewal equation; self-similar measures; -dimension; -density; locally compact abelian groups; vector-valued measures; convolution powers; Markov chains; theorem of Deny
UR - http://eudml.org/doc/216238
ER -

References

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