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Products of non-stationary random matrices and multiperiodic equations of several scaling factors

Fan, AH; Saussol, B and Schmeling, Jörg LU (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.
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author
organization
publishing date
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
2007-10-22 17:48:49
date last changed
2017-12-10 04:29:24
@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},
  volume       = {214},
  year         = {2004},
}