On Geometry of the Unit Ball of Paley–Wiener Space Over Two Symmetric Intervals

Abstract

Abstract Let $PW_S^1$ be the space of integrable functions on ${\mathbb {R}}$ whose Fourier transform vanishes outside $S$, where $S = [-\sigma ,-\rho ]\cup [\rho ,\sigma ]$, $0<\rho <\sigma $. In the case $\rho>\sigma /2$, we present a complete description of the set of extreme and the set of exposed points of the unit ball of $PW_S^1$ . The structure of these sets becomes more complicated when $\rho <\sigma /2$.