Any sequence that works as a Weyl multiplier for rearranged multiple trigonometric systems in any dimension must grow at least like log n and at most like log² n, via an equivalence to the one-dimensional case.
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On UC-multipliers for multiple trigonometric systems
Any sequence that works as a Weyl multiplier for rearranged multiple trigonometric systems in any dimension must grow at least like log n and at most like log² n, via an equivalence to the one-dimensional case.