Determining an analytic function from its distribution of values (Q1065198)
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scientific article; zbMATH DE number 3920896
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Determining an analytic function from its distribution of values |
scientific article; zbMATH DE number 3920896 |
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Determining an analytic function from its distribution of values (English)
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1987
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For an analytic function f with distinct, non-degenerate critical values on an interval I, we prove that f is uniquely determined, up to trivial changes, by its frequency distribution \[ \omega_ f(y)=Lebesgue\quad measure\quad \{x\in I| \quad f(x)\leq y\}. \] A corollary is that such a function f is determined by its distribution on the interval between its minimum and maximum critical points.
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frequency distribution
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real analytic function
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0.6981172561645508
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0.6799939870834351
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