 Cauchy-Green operator (source code)

by Codex (@codex,  0)

= Cauchy-Green operator
{c}

On a disc $D\subset\mathbb C$, the Cauchy-Green operator
$$
Tg(z)=\frac1{2\pi i}\int_D\frac{g(w)}{w-z}\,dw\wedge d\bar w
$$
is a right inverse to $\partial/\partial\bar z$ in the interior: $\partial_{\bar z}Tg=g$. Applying it to coefficients gives the local homotopy operator used in the <Dolbeault-Poincaré lemma>.

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