Majorants and extreme points of unit balls in Bernstein spaces (Q1881759)

The Bernstein space \(B^1(\sigma)\) (\(\sigma >0\)) is the closed subspace of \(L^1(\mathbb R)\) consisting of functions having Fourier transforms (in the sense of generalized functions) supported in \([-\sigma,\sigma]\). In this paper, the author first exhibits a predual of \(B^1(\sigma)\) and then shows that the extreme points of the unit ball are precisely functions of the form \(\omega B_{\omega A}\), where \(\omega \in B^1(\sigma)\) is a \(\sigma\)-majorant with \(\| \omega\| = 1\) and \(B_{\omega A} \) is an exact partial Blaschke product of \(\omega\) corresponding to some set \(A\) of zeros of \(\omega\).