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

AH Fan, B Saussol, Jörg Schmeling

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Sammanfattning

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.
Originalspråkengelska
Sidor (från-till)31-54
TidskriftPacific Journal of Mathematics
Volym214
Nummer1
StatusPublished - 2004

Ämnesklassifikation (UKÄ)

  • Matematik

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