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- W1570334520 abstract "Let Ω1, Ω2 be open subsets of ℝequation/tex2gif-sup-1.gif and ℝequation/tex2gif-sup-2.gif , respectively, and let A(Ω1) denote the space of real analytic functions on Ω1. We prove a Glaeser type theorem by characterizing when a composition operator Cφ : A(Ω1) → A(Ω2), Cφ(f) ≔ f ∘ φ, is a topological embedding. Using this result we characterize when A(Ω1) can be embedded topologically into A(Ω2) as a locally convex space or as a topological algebra. We also characterize LB–subspaces and Fréchet subspaces of A(Ω1). In particular, it follows that if A(Ω1) and A(Ω2) are isomorphic as locally convex spaces, then d1 = d2." @default.
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- W1570334520 date "2003-06-01" @default.
- W1570334520 modified "2023-10-18" @default.
- W1570334520 doi "https://doi.org/10.1002/mana.200310053" @default.
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