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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

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The operator $(\partial_x+i\partial_y)(\partial_x-i\partial_y)^{-1}$

So I found this operator while messing around with the equations of 2D incompressible fluid mechanics (it relates to the pressure Hessian). Specifically, if we call it $K$, then $$ K\Delta p = (p_{xx …