Exposedness in Bernstein spaces - Norvidas, Saulius (Lietuvos matematikos rinkinys, 2007)
The Bernstein space Bσp, σ > 0, 1 ≤ p ≤ ∞, consists of those Lp(R)-functions whose Fourier transforms are supported on [-σ, σ]. Every function in Bσp has an analytic extension onto the complex plane C which is an entire function of exponential type at most σ . Since Bσp is a conjugate Banach space, its closed unit ball D(Bσp) 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(Bσ1) and illustrate them by several examples.
Keywords: Bernstein spaces; entire functions of exponential type; sine-type functions; exposed points