Menshov表示谱
Menshov representation spectra
摘要：
Menshov谱是整数的子集，其足以将每个可测函数表示为几乎处处收敛的三角（非傅立叶）和。在这种语言中，著名的“Menshov表示定理”指出Z是Menshov谱。本文构造了1）几乎指数稀疏的Menshov谱2）几乎平方的Menshov谱。然后我们证明了正整数不是Menshov谱，而是测度Menshov谱，并在解析设置中重复1）和2）。
英文摘要：
A Menshov spectrum is a subset of the integers that is sufficient for representing every measurable function as an almost-everywhere converging trigonometric (non-Fourier) sum. In this language the celebrated "Menshov representation theorem" states that Z is a Menshov spectrum. In this paper we construct 1) Menshov spectra that are almost exponentially sparse 2) that are almost squares. Then we show that the positive integers are not a Menshov spectrum but are a Menshov spectrum in measure, and repeat 1) and 2) in the analytic settings.
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