An extremal problem for Fourier transforms of probabilities (Q2565525)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An extremal problem for Fourier transforms of probabilities |
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An extremal problem for Fourier transforms of probabilities (English)
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27 September 2005
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Let \(\Phi\) be the set of all characteristic functions of one-dimensional probability distributions, \(\Phi_T=\{\varphi\in\Phi:\varphi(T)=0\}\), \(T>0\), and \(M_T(t)=\sup_{\varphi\in\Phi_T}| \varphi(t)| \). Then \(M_T(t)=\cos (\pi t/2T)\) if \(T/t\) is integer and \(M_T(t)=1\) otherwise.
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characteristic function
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survival amplitude
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