Does $\delta(x^n)$ make sense? I guess that naively we could define, for example for $n=2$: $$\delta(x^2)=\lim_{a\rightarrow0}\frac{1}{2|a|}(\delta(x-a)+\delta(x+a))$$
But it seems to me that it would make any integral diverges.
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1Are you using this? – J.G. Sep 12 '21 at 11:21
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1You are correct that $\delta(x^n)$ doesn't make sense for $n>1$ or for any $\delta(f(x))$ having $f'(0)=0.$ – md2perpe Sep 12 '21 at 11:38