What is one example of pseudodifferential operator $P$ that smooth out the singularity of delta function, i.e. $P$ s.t. $P \delta(x) \in C^{\infty}(\mathcal{R})$?
2026-03-25 12:37:17.1774442237
Example of pseudodifferential operators that smooth out the singularity of delta function
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The Fourier transform of the delta distribution is a constant function. Thus, if you Fourier transform, multiply with a Schwartz function and Fourier transform back, you get a Schwartz function.