Abstract

Let β > 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

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 β is a Pisot–Vijayaraghavan number is well studied.

Authors