Exposedness in Bernstein spaces

Abstract

The Bernstein space B_σ^p, σ > 0, 1 \leq p \leq ∞, consists of those L^p(R)-functions whose Fourier transforms are supported on [-σ, σ]. Every function in B_σ^p has an analytic extension onto the complex plane C which is an entire function of exponential type at most σ . Since B_σ^p is a conjugate Banach space, its closed unit ball D(B_σ^p) has nonempty sets of both extreme and exposed points. These sets are nontrivially arranged only in the cases p = 1 and p = ∞. In this paper, we investigate some properties of exposed functions in D(B_σ¹) and illustrate them by several examples.