 First-order Cauchy-Riemann operator (source code)

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= First-order Cauchy-Riemann operator
{title2=$\partial_{\bar z}$}

The first-order Cauchy-Riemann operator on two real variables is $\partial_{\bar z}=\tfrac12(\partial_{x_1}+i\partial_{x_2})$. It is a scalar complex <elliptic differential operator>, since its <principal symbol> has nonzero modulus at every nonzero real frequency.

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