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# 7. Suppose f: D→C is holomorphic. Show that the diameter d= sup,, wED f(a)-f(w)of the image of f ... 7. Suppose f: D→C is holomorphic. Show that the diameter d= sup,, wED f(a)-f(w)of the image of f satisfies Moreover, it can be shown that equality holds precisely when f is linear, f(z)- Note. In connection with this result, see the relationship between the diameter of a curve and Fourier seri . es described in Problem 1, Chapter 4, Book I -, Layer d' whenever 0

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