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Could You help me? Where $g(t)$ is Cantor function: $$G(\omega)= \int_0^1 e^{2\pi i\omega t}dg(t)$$ Show, that $G(\omega)\not\to0$, if $\omega\to\infty$

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Just to be sure: you meant $g(t)$ to be this Cantor function? –  Willie Wong May 30 '13 at 14:32
yes. All right. –  user80192 May 30 '13 at 14:39
One way is to use the self-similarity of the Cantor set. The scaling property ensures that if $G(3^k) = G(1)$. An you boil it down to computing the coefficient $G(1)$ and checking that it is not zero. –  Willie Wong May 30 '13 at 14:58

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