Positive definiteness of a family of functions (Q2396418)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive definiteness of a family of functions |
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Positive definiteness of a family of functions (English)
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8 June 2017
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Let \(\rho\) be a norm on \(\mathbb R^n\) and \(w,z\in\mathbb C\). Conditions for \(w, z\) are given for the positive definiteness of the function \(x\mapsto f_{w,z}(\rho(x))\), where \(f_{w,z}(t)=\mathrm{Re}(we^{-zt})\). Some conditions hold for \(\|\cdot\|_1,\;\|\cdot\|_2\) or \(n=2\) only.
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positive definite functions
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Bochner's theorem
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