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Mar 9, 2021 at 8:53 comment added Anixx I am judging from the Fourier transform-based definition. Yes, it seems not symmetric under rotations.
Mar 9, 2021 at 8:48 comment added bathalf15320 If you are seriouly claiming that the delta distribution is NOT symmetric under rotations, then I'm outta here!
Mar 9, 2021 at 8:43 history edited bathalf15320 CC BY-SA 4.0
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Mar 9, 2021 at 8:32 comment added Anixx Also, according to the linked result, $\int_{-\infty}^\infty \delta(t+bi)f(t)dt=f(-bi)\ne f(bi)=\int_{-\infty}^\infty \delta(t-bi)f(t)dt$
Mar 9, 2021 at 8:26 comment added Anixx How it is symmetric with respect to rotation if $\delta(i) = \frac{1}{2\pi}\int_{-\infty}^\infty e^{-t}\, dt$, which is divergent to infinity, while $\delta(1)=0$?
Mar 9, 2021 at 8:20 history answered bathalf15320 CC BY-SA 4.0