Abstract
We propose necessary and sufficient conditions for a distribution (generalized function) $f$ of several variables to be positive definite. For this purpose, certain analytic extensions of $f$ to tubular domains in complex space $\mathbb{C}^n$ are studied. The main result is given in terms of completely monotonic functions on convex cones in $\mathbb{R}^n$.
Citation
Saulius Norvidas . "On positive definite distributions with compact support." Banach J. Math. Anal. 9 (3) 14 - 23, 2015. https://doi.org/10.15352/bjma/09-3-2
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