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We present a result on existence of some kind of peak functions for$\C$-convex domains and for the symmetrized polydisc. Then we apply the latterresult to show the equivariance of the set of peak points for $A(D)$ underproper holomorphic mappings. Additionally, we present a description of the setof peak points in the class of bounded pseudoconvex Reinhardt domains.

Proper holomorphic mappings vs. peak points and Silov boundary