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**is there any counterexample to this ??**

let be the Fourier transform

[tex] G(s) = \int_{-\infty}^{\infty}dxf(x)exp(isx) [/tex]

with the properties

[tex] f(x) [/tex] and [tex] D^{2}f(x) [/tex] are EVEN funnctions of 'x'

[tex] f(x) > 0 [/tex] and [tex] D^{2}f(x) > 0 [/tex] on the whole interval (-oo,oo)

then G(s) has only REAL roots

is there any counterexample to this ?? thanks