## under

Under what conditions can $f$ have a local minimum in $A$?

Then $X$ is a Banach algebra under convolution multiplication $\langle$under this norm$\rangle$.

It follows that $G$ is maximal under $\langle$for$\rangle$ the usual partial ordering of $B$.

Hence $F$ is invariant under $\phi$. [= $\phi$-invariant]

the image of $A$ under $f$ = the $f$-image of $A$

The point $x$ maps to $\infty$ under $f$.

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