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How to solve the following $0= \int_{-\infty}^\infty e^{-\frac{(bt+\omega)^2}{2}} f(t+\omega...

$\omega$-dependent solutions are not interesting, since after the substitution $t=x-\omega$ $$0=PV\int_{-\infty}^\infty e^{-\frac{\left(b(x-\omega)+\omega\right)^2}{2}} \frac{f(x)}{i(x-\omega)} \, {\r …
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