On exposed functions in Bernstein spaces |
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Authors: | S Norvidas |
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Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania |
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Abstract: | For σ > 0, the Bernstein space {ie427-01} consists of those L
1(ℝ) functions whose Fourier transforms are supported by −σ, σ]. Since {ie427-02} is separable and dual to some Banach space, the closed unit ball {ie427-03} of {ie427-04} has sufficiently
large sets of both exposed and strongly exposed points: {ie427-05} coincides with the closed convex hull of its strongly exposed
points. We investigate some properties of exposed points, construct several examples, and obtain as corollaries relations
between the sets of exposed, strongly exposed, weak* exposed, and weak* strongly exposed points of {ie427-06}. |
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Keywords: | Fourier transforms band-limited functions entire functions of exponential type sine-type entire functions extreme points exposed points strongly exposed points |
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