- #1
zetafunction
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- 0
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
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