科研之友
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摘要
We prove that for an ergodic rotation and square integrable function on a compact abelian group, the ergodic process is uniquely determined by its two-dimensional laws if the same holds for the process for some real bounded function such that all Fourier-Stieltjes coefficients of are non null. Applied to the one or two dimensional torus, this result gives a large class of such processes, for instance any process given by non constant monotone continuous function, or having a discontinuity at an irrational point, on the unit interval, is in the corresponding class. We also prove that all Fourier coefficients of such a monotone function are non null.
- 出版日期2015-2
