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Notes on the Szegő minimum problem. I. Measures with deep zeroes
Israel Journal of Mathematics ( IF 0.8 ) Pub Date : 2020-10-01 , DOI: 10.1007/s11856-020-2077-x
Alexander Borichev , Anna Kononova , Mikhail Sodin

The classical Szego polynomial approximation theorem states that the polynomials are dense in the space $L^2(\rho)$, where $\rho$ is a measure on the unit circle, if and only if the logarithmic integral of the measure $\rho$ diverges. In this note we give a quantitative version of Szego's theorem in the special case when the divergence of the logarithmic integral is caused by deep zeroes of the measure $\rho$ on a sufficiently rare subset of the circle.

中文翻译:

关于 Szegő 最小问题的注释。一、深零的措施

经典的 Szego 多项式逼近定理指出多项式在空间 $L^2(\rho)$ 中是稠密的,其中 $\rho$ 是单位圆上的测度,当且仅当该测度的对数积分 $\ rho$ 发散。在这篇笔记中,我们给出了 Szego 定理的量化版本,在特殊情况下,当对数积分的发散是由圆的一个足够稀有的子集上的度量 $\rho$ 的深零引起的。
更新日期:2020-10-01
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