By using the Ascoli-Arzela theorem, show that the functions fn(z) = zn in Δ(1) n = 1, 2,..., are not equicontinuous.
A family F of complex-valued functions on A is called equicontinuous if ∀ε > 0, ∃δ > 0 such that |f(z) - f(w)| < ε, ∀z, w ∈ A with |z - w| < δ, ∀ f ∈ F.
There's actually a bar over the complex unit disk symbol. Is it the conjugate set? I'm not quite sure.
A family F of complex-valued functions on A is called equicontinuous if ∀ε > 0, ∃δ > 0 such that |f(z) - f(w)| < ε, ∀z, w ∈ A with |z - w| < δ, ∀ f ∈ F.
There's actually a bar over the complex unit disk symbol. Is it the conjugate set? I'm not quite sure.