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Let F ∈ C1(Ω,C) be a not necessarily open function on a Euclidean manifold Ω such that F obeys the strong maximum modulus principle in a bilateral sense defined in the paper and does not attain weak local minimum on a submanifold M ⊂ Ω. We prove that the polynomial ring C[F ] satisfies the strong maximum modulus principle on M. We also give a sufficient condition for subspaces of polyanalytic functions to have constant modulus spaces containing only constants. Mathematics Subject Classification: 30C80, 30A99, 46E25

Some maximum modulus polynomial rings and constant modulus spaces