Plurisubharmonic function: Difference between revisions

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'''Relation to Dirac Delta:''' On 1-dimensional complex Euclidean space <math>\mathbb{C}^1</math> , <math>u(z) = \log(z)</math> is plurisubharmonic. If <math>f</math> is a C<sup>∞</sup>-class function with [[compact support]], then [[Cauchy integral formula]] says
::<math>f(0)=-\frac{\sqrt{-1}}{2\pi}\int_Cint_D\frac{\partial f}{\partial\bar{z}}\frac{dzd\bar{z}}{z}</math>
which can be modified to
::<math>\frac{\sqrt{-1}}{\pi}\partial\overline{\partial}\log|z|=dd^c\log|z|</math>.