Substitute $\omega = u^2$ and consider the resulting expression as

$$-2 \frac{\partial}{\partial r} \int_0^{\infty} du \, e^{-r u} \, e^{i t u^2}$$

The integral will end up being some sort of error function of complex argument; the derivative may invoke a more elementary expression, but likely not.

Inverse fourier transform of exponentially decaying function in the frequency domain
When the text of a QRcode comes from a \newcommand{\TextInsideQRcode}, the spaces between the words vanish. Is there a way to maintain the spaces between the words ?

 \documentclass[]{article}
 \usepackage[]{qrcode}
 \begin{document}

 \newcommand{\TextInsideQRcode}[0]{Here is a newcommand that contains the verbatim text inside the qr code\? In the resulting  QRcode, the spaces between the words vanish. \? Is there a way to maintain the spaces between the words ?} %

 \qrcode[]{\TextInsideQRcode}% 

 \vglue1cm

 \qrcode[]{When a similar verbatim text in directly entered into the qrcode command, the spaces between the words remain intact.}% 

 \end{document}



