  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.
