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Jun 1, 2017 at 20:09 history bounty ended CommunityBot
May 30, 2017 at 17:26 comment added AccidentalFourierTransform Perhaps interesting as well: if we use a finite difference instead of a derivative, we have $\Delta^d_\ell N=0$, $\Delta^{d-1}_\ell N=2$, $\Delta^{d-2}_\ell N=2 d+2 \ell-3$, $\Delta^{d-3}_\ell N=(d+\ell-2)^2$, etc.
May 29, 2017 at 17:21 comment added user4552 This reads to me as a rewording of the argument I made in the fourth paragraph of the question. There are some added details, but most of those added details were already worked out in the comment by AccidentalFourierTransform. The reason I posted this as a question and offered a bounty was that I was hoping someone could come at this from a different angle.
May 28, 2017 at 22:46 history edited Prahar CC BY-SA 3.0
added 251 characters in body
May 28, 2017 at 21:36 history answered Prahar CC BY-SA 3.0