On the maximum modulus principle and the identity theorem in arbitrary dimension. (English) Zbl 1538.32003
Summary: We prove an identity theorem for Gâteaux holomorphic functions on polygonally connected 2-open sets, which yields a very general maximum norm principle and a sublinear “max-min” principle. All results apply in particular to vector-valued functions which are holomorphic (in any sense that implies Gâteaux holomorphy) on domains in Hausdorff locally convex spaces.
MSC:
32A10 | Holomorphic functions of several complex variables |
32K12 | Holomorphic maps with infinite-dimensional arguments or values |
46G20 | Infinite-dimensional holomorphy |