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Dec 8, 2016 at 13:21 history edited Abdelmalek Abdesselam CC BY-SA 3.0
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Dec 7, 2016 at 20:07 comment added Abdelmalek Abdesselam @Sergei: thanks for pointing out the work of Zastavnyi. However, the latter seems to consider the (more difficult) case where the norm involved is $L^p$ with $p>2$ on $\mathbb{R}^n$, $n\ge 2$.
Dec 7, 2016 at 6:12 comment added Sergei Due to information in 2013 V.P.Zastavny thesis a problem was first in more general form formulated in Schoenberg,1938,Tran.AMS 44. Interesting generalizations are in Zastavnyi V. P. Positive definite functions depending on the norm / V. P. Zastavnyi // Russian J. Math. Physics. – 1993. – Vol. 1,ð4. – P. 511– 522. and Koldobskii : mathnet.ru/php/…
Dec 6, 2016 at 18:19 history edited Abdelmalek Abdesselam CC BY-SA 3.0
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Dec 6, 2016 at 18:05 history edited Abdelmalek Abdesselam CC BY-SA 3.0
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Dec 6, 2016 at 17:39 history answered Abdelmalek Abdesselam CC BY-SA 3.0