Koldobskij, A. L. The Schoenberg problem on positive definite functions. (Russian) Zbl 0741.60010 Algebra Anal. 3, No. 3, 78-85 (1991). For every \(n\geq 3\), \(q>2\), \(\beta>0\), the function \(\exp(-(| x_ 1|^ q+\dots+| x_ n|^ q)^{\beta/q})\) is not positive definite. This result gives an answer to I. J. Schoenberg’s question posed in [Trans. Am. Math. Soc. 44, 522-536 (1938; Zbl 0019.41502)]. Reviewer: A.L.Koldobskij (St.Petersburg) Cited in 2 ReviewsCited in 11 Documents MSC: 60E10 Characteristic functions; other transforms 42A82 Positive definite functions in one variable harmonic analysis Keywords:Fourier transform; positive definite functions; distributions Citations:Zbl 0019.41502 PDFBibTeX XMLCite \textit{A. L. Koldobskij}, Algebra Anal. 3, No. 3, 78--85 (1991; Zbl 0741.60010)