In such disparate contexts as the Hahn-Banach theorem, seminorms, Kol-mogorov’s theorem (cf. 6.162), von Neumann’s theory of almost periodic functions on groups (cf. 2.93), his theory of games [NM] and linear programming, Jensen’s inequality, Hadamard’s three-lines/three-circles theorems, the Hausdorff-Young theorem, probability theory, etc., the rôle played by convexity is central. The following discussion attempts to illustrate that role in complex analysis.
KeywordsConvex Function Maximum Principle Convex Subset Finite Interval Compact Abelian Group
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