Schoenberg's Problem on Positive Definite Functions

Details Schoenberg's Problem on Positive Definite Functions Schoenberg's Problem on Positive Definite Functions

1992-10-19

arxiv.org/abs/math/9210207v1

Mathematics

Functional Analysis

Scientific paper

If $n \ge 3$, $q>2$ and $\beta > 0$ then the function
$\exp(-(|x_1|^q+|x_2|^q+\dots+|x_n|^q)^{\beta/q})$\ is not positive definite.
This result gives an answer to a question posed by I.J.~Schoenberg in 1938.
This text is an authorized English translation of the paper published in
Russian in Algebra and Analysis 3(1991), \#3, p.78--85.

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