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Examining the Hilbert transform of functions over the positive real line

$\DeclareMathOperator\supp{supp}$Let $H:L^{2}(\mathbb{R})\to L^{2}(\mathbb{R})$ be the Hilbert transform. Let suppose we have a compaclty supported function $f \in L^{2}(\mathbb{R})$ such that $\supp(...
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0 answers
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Particular Ehrenpreis factorization for covariance function

Let $f:\mathbb{R}^d\to\mathbb{R}$ be a smooth compactly supported covariance function of a stationary random fields (hence positive definite). Is there a compactly supported function $g:\mathbb{R}^d\...