Harold wrote: << Quoting Mike Stay <metaweta@gmail.com>: << Is there a general formula for "d/dz" in dimension D? You are in good company with Paul Dirac and Oliver Heaviside. As long as D is finite, there is no problem, even with a multiply valued complex logarithm. It is the limit that hurts, and for which distribution theory was sort of invented. I recall that in the late forties, Aurel Wintner proved that there are no matrices A and B such that AB - BA = I, the unit matrix. . . . . . .
Can someone please elaborate? I'm not getting the connection between Mike's question and being in good company with anyone, or with a complex logarithm, or with the equation AB - BA = I. Since Mike first mentioned that exp(d/dz)(f)(z) = f(z+1) (presumably on R or C), I thought he was looking for a D-dimensional analogue of this formula. No? If Harold's comment addresses this, apologies but I'm missing it. On the other hand, I haven't received Harold's post directly but only because Gene quoted it. Maybe I've missed some other intervening posts as well? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele