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- W3207560243 abstract "In this note I prove the following property of Herglotz functions, which to my knowledge is new: For a Herglotz function $h(z)$ and a real number $r in mathbb R$ define a Herglotz function $g_r(z) = (r - h(z))^{-1}.$ Let $mu_r^{(s)}$ be the singular part of the measure $mu_r$ which corresponds to $g_r(z)$ via the Herglotz representation theorem. Then the measure $int_0^1 mu_r^{(s)},dr$ is absolutely continuous, its density is integer-valued a.e., and moreover the density takes values $0$ or $1$ a.e." @default.
- W3207560243 created "2021-10-25" @default.
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- W3207560243 date "2021-10-09" @default.
- W3207560243 modified "2023-09-27" @default.
- W3207560243 title "On a property of Herglotz functions." @default.
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