Analytic capacity for two segments

The analytic capacity γ(E) of a compact set E in the complex plane C is defined by γ(E) = sup , where — f′(∞) is the 1/z-coeffieient of f(ζ) at infinity and the supremum is taken over all bounded analytic functions f(ζ) outside E with supremum norm less than or equal to 1. Analytic capacity γ(·) plays various important roles in the theory of bounded analytic functions.