Differential Criteria for Positive Definiteness
نویسنده
چکیده
We show how the Mellin transform can be used to derive differential criteria for integral representations of functions as scale mixtures, and apply this idea to derive differential criteria for positive definiteness of functions in a manner similar to that of Gneiting (1999,2001). We also give a simple derivation of Williamson’s result on multiply monotone functions (Williamson, 1956), with a limiting process giving the Bernstein-Widder theorem.
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