On geometry of the unit ball of Paley-Wiener space over two symmetric intervals

Abstract

Let $P{W}_S^1$ 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 $P{W}_S^1$. The structure of these sets becomes more complicated when $\rho <\sigma /2$.

28 pages, the description of exposed points is added

References in corpus (2)

• Lacunary polynomials in $L^1$: geometry of the unit sphere
• Nearly outer functions as extreme points in punctured Hardy spaces