Definition talk:Partial Differential Operator

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This definition seems specifically geared for complex analysis, but it's difficult to work out as the notation is not explained. In any case, other contexts (e.g. real) number plane) need to be included. Not sure, as I have not fully understood it as it stands.

It works in general for multidimensional analysis; the codomain of the fns is the only difference. Merge with Partial Derivative strongly discouraged, this is wholly different conceptually.
I also disagree with the merger: for example there's no linearity (or even continuity of coefficients) here: I just wrote down the most general definition possible: it's pretty useless without further assumptions.
I think two definitions for $\R$ / $\C$ is excessive: $\C$ just allows schrodinger operators and whatnot as well; since it's an equation on $\R^n$ it's still real analysis. I'm fine with putting $\R$ as the image space if that's preferred.
Possibly a separate definition of linear operators with constant coefficients would be better? I don't know anything about any other kind anyway. --Linus44 (talk) 21:35, 16 October 2012 (UTC)
Changed to $\R$, as differentiability isn't defined into $\C$. --Linus44 (talk) 21:38, 16 October 2012 (UTC)
That last amendment makes me more comfortable - apologies, I'm slightly out of my depth. Keep the pages separate, no worries. --prime mover (talk) 22:17, 16 October 2012 (UTC)