Open AccessExposedness in Bernstein spaces
Author(s) -
Саулюс Норвидас
Publication year - 2007
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2007.19767
Subject(s) - mathematics , banach space , exponential function , extension (predicate logic) , unit sphere , analytic function , pure mathematics , space (punctuation) , complex plane , ball (mathematics) , function (biology) , fourier transform , mathematical analysis , combinatorics , computer science , evolutionary biology , biology , programming language , operating system
The Bernstein space Bσp, σ > 0, 1 \leq p \leq ∞, 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.