Polynomials and entire functions: Zeros and geometry of the unit ball (Q1588354)

Let X be a Banach space and \[ b(X):=\{x\in X;\;\|x\|=1\}. \] An element \(x\in b(X)\) is an extreme point of \(b(X)\) if it is not a proper convex combination of two distinct points in \(b(X)\), and \(x\in b(X)\) is an exposed point of \(b(X)\) if there exists a functional \(\Phi\in X^*\) such that \(\|\Phi\|= 1\) and \(\Phi = 1\) in \(b(X)\) only on \(x\). The author has given the complete characterization of such points in certain \(L^1\)-spaces of polynomials and entire functions.