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- W2043041545 abstract "We provide a new simple proof to the celebrated theorem of Poltoratskii concerning ratios of Borel transforms of measures. That is, we show that for any complex Borel measure μ on R and any f∈L1(R,dμ),limε→0(Ffu(E+iε)/Fμ(E+iε))=f(E) a.e. w.r.t. μsing, where μsing is the part of μ which is singular with respect to Lebesgue measure and F denotes a Borel transform, namely, Ffμ(z)=∫(x−z)−1f(x)dμ(x) and Fμ(z)=∫(x−z)−1dμ(x)." @default.
- W2043041545 created "2016-06-24" @default.
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- W2043041545 date "2004-10-01" @default.
- W2043041545 modified "2023-09-23" @default.
- W2043041545 title "A new proof of Poltoratskii's theorem" @default.
- W2043041545 cites W184103009 @default.
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- W2043041545 doi "https://doi.org/10.1016/j.jfa.2003.09.014" @default.
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