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Can somebody explain the use of ange brackets in the book I'm reading now? On pages 1–2 of Krantz's Function theory of several complex variables (2nd ed., 1992), I see the following: if $dz_j=dx_j+i\,dy_j$ is a differential and $\frac{\partial}{\partial z_j}=\frac12\Bigl(\frac{\partial}{\partial x_j}+i\frac{\partial}{\partial y_j}\Bigr)$ is a partial differential operator, then $\Bigl\langle{dz_j,\frac{\partial}{\partial z_j}}\Bigr\rangle=1$. What is this operation called? An inner product of a differential form and a differential operator? What should I google for? Any explanatory books?

Andrei Zorine
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  • I think it goes under the name pairing and stands for $$\Bigl\langle{dz_j,\frac{\partial}{\partial z_j}}\Bigr\rangle := dz_j\left( \frac{\partial}{\partial z_j}\right)$$ I read this a few times in books on differential geometry. It is a special case of interior multiplication. – TheGeekGreek Sep 10 '17 at 14:51

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