Products of non-stationary random matrices and multiperiodic equations of several scaling factors
(2004) In Pacific Journal of Mathematics 214(1). p.31-54- Abstract
- Let beta > 1 be a real number and M : R --> GL(C-d) be a uniformly almost periodic matrix-valued function. We study the asymptotic behavior of the product P-n(x) = M(beta(n-1)x)...M(betax) M(x). Under some conditions we prove a theorem of Furstenberg-Kesten type for such products of non-stationary random matrices. Theorems of Kingman and Oseledec type are also proved. The obtained results are applied to multiplicative functions defined by commensurable scaling factors. We get a positive answer to a Strichartz conjecture on the asymptotic behavior of such multiperiodic functions. The case where is a Pisot-Vijayaraghavan number is well studied.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/286286
- author
- Fan, AH ; Saussol, B and Schmeling, Jörg LU
- organization
- publishing date
- 2004
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Pacific Journal of Mathematics
- volume
- 214
- issue
- 1
- pages
- 31 - 54
- publisher
- Pacific Journal of Mathematics
- external identifiers
-
- wos:000189187500004
- scopus:1842682947
- ISSN
- 0030-8730
- language
- English
- LU publication?
- yes
- id
- aa5ed9c0-f9a3-43cc-a2e8-3b0d3486a844 (old id 286286)
- alternative location
- http://pjm.math.berkeley.edu/pjm/2004/214-1/p04.xhtml
- date added to LUP
- 2016-04-01 15:59:08
- date last changed
- 2022-01-28 08:27:59
@article{aa5ed9c0-f9a3-43cc-a2e8-3b0d3486a844,
abstract = {{Let beta > 1 be a real number and M : R --> GL(C-d) be a uniformly almost periodic matrix-valued function. We study the asymptotic behavior of the product P-n(x) = M(beta(n-1)x)...M(betax) M(x). Under some conditions we prove a theorem of Furstenberg-Kesten type for such products of non-stationary random matrices. Theorems of Kingman and Oseledec type are also proved. The obtained results are applied to multiplicative functions defined by commensurable scaling factors. We get a positive answer to a Strichartz conjecture on the asymptotic behavior of such multiperiodic functions. The case where is a Pisot-Vijayaraghavan number is well studied.}},
author = {{Fan, AH and Saussol, B and Schmeling, Jörg}},
issn = {{0030-8730}},
language = {{eng}},
number = {{1}},
pages = {{31--54}},
publisher = {{Pacific Journal of Mathematics}},
series = {{Pacific Journal of Mathematics}},
title = {{Products of non-stationary random matrices and multiperiodic equations of several scaling factors}},
url = {{http://pjm.math.berkeley.edu/pjm/2004/214-1/p04.xhtml}},
volume = {{214}},
year = {{2004}},
}