On quotients of positive definite functions (Q5932740)
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scientific article; zbMATH DE number 1604298
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On quotients of positive definite functions |
scientific article; zbMATH DE number 1604298 |
Statements
On quotients of positive definite functions (English)
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13 June 2001
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Let \(E'\) be the space of distributions with compact support and \(S\) be the space of complex valued Schwartz functions. The main result is: Let \(f:\mathbb R\to \mathbb R\) be the Fourier transform of a real \(T\in E'\). Then \(f\) is the quotient of two positive definite functions from \(S\) if and only if \(f(0)\neq 0\).
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positive definite functions
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Schwartz functions
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distributions
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Fourier-Laplace transform
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