Fourier transform of a lorentzian function

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The Fourier transform of a Lorentzian function results in a decaying oscillation, not another Lorentzian. In contrast, the Fourier transform of a Gaussian function remains a Gaussian. The discussion raises a question about whether the Fourier transform of the second derivative of a Lorentzian function also yields a second derivative of a Lorentzian. Participants suggest exploring theorems related to the Fourier transform of derivatives for further insights. Understanding these relationships is crucial for analyzing the behavior of these functions in frequency space.
zak8000
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hi

I know the Fourier transform of a lorentzian function is a lorentzian but i was wondering if the Fourier transform of the second derivation of a lorentzian function is also a second derivative of a lorentzian function

Thanks
 
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The Fourier transform of a Lorentzian isn't a Lorentzian (its a decaying oscillation)

The Fourier transform of a Gaussian is a Gaussian, which is I guess what you mean?

Do you know any theorems about the Fourier transform of a derivative to help answer your other question?
 

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