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- W2554678983 abstract "One can easily prove that in the case of the Bergman boundary it suffices to check that max K |f | = max D |f | for every f ∈ O(D). Obviously, B(D) ⊂ A(D). In particular, ∂BD ⊂ ∂SD ⊂ ∂D. Notice that in general ∂BD ∂SD, e.g. if D := {(z, w) ∈ D∗ × C : |w| < |z|− log |z|} ⊂ D∗ × D, then T = ∂BD {D× C : |w| = |z|− log |z|} = ∂SD. Assume that the envelope of holomorphy D of D is univalent. It is well-known that supD |g| = supD |g| for every g ∈ O(D). In particular, D is bounded. Take a g ∈ A(D) (resp. g ∈ B(D)) and let C := max ∂SD |g| (resp. C := max ∂BD |g|). Since A(D)|D ⊂ A(D)" @default.
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- W2554678983 date "2013-01-01" @default.
- W2554678983 modified "2023-09-26" @default.
- W2554678983 title "A COUNTEREXAMPLE TO BREMERMANN'S THEOREM ON SHILOV BOUNDARIES" @default.
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