论文标题
关于指数类型功能的伯恩斯坦空间中暴露的功能
On exposed functions in Bernstein spaces of functions of exponential type
论文作者
论文摘要
对于$σ> 0 $，Bernstein Space \ $ b^1_σ$由$ l^1（r）$ \函数组成，其傅立叶变换由$ [ - σ，σ] $支持。由于$ b^1_σ$可分开且双重与某些BANACH空间，因此$ b^1_σ$ \的封闭式单位球$ d（b^1_σ）$具有足够大的暴露和强烈暴露点。此外，$ d（b^1_σ）$与其强烈暴露点的封闭凸面相吻合。我们研究了裸露点的一些属性，构造了几个示例，并作为推论获得了暴露，强烈暴露，弱$^{\ ast} $的关系，而弱$^{\ ast} $强烈暴露了$ d（b^1_σ）$。
For $σ>0$, the Bernstein space \ $B^1_σ$ consists of those $L^1(R)$\ functions whose Fourier transforms are supported by $[-σ,σ]$. Since $B^1_σ$ is separable and dual to some Banach space, the closed unit ball $D(B^1_σ)$ of $B^1_σ$\ has sufficiently large sets of both exposed and strongly exposed points. Moreover, $D(B^1_σ)$ 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 the relations between the sets of exposed, strongly exposed, weak$^{\ast}$ exposed, and weak$^{\ast}$ strongly exposed points of $D(B^1_σ)$.
