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Partial differential equations question whats th
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\[S[f](\omega)=\frac{2}{\pi}\ \int\limits_{0}^{\infty} f(x)(\sin(\omega x)dx\] \[f(x) = \int\limits_{0}^{\infty}f(x)(\omega)\sin(\omega x)d\omega\] under what conditions \(f)\) does S\( ~[f] \) exist
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