Bochner-Lebesgue空间内的最佳同时逼近（英文）
发布时间：2018-11-15 13:05
【摘要】：在本文中,我们研究了Bochner-Lebesgue空间内的相对于欧氏空间的Minkowski范数的最佳同时逼近.首先,给出了由距离函数表示的最佳同时逼近的刻画.然后,利用可测选择定理证明其函数取值于一个闭的可分子空间的Bochner-Lebesgue空间,其同时可逼近性等价于此闭的可分子空间的同时可逼近性.最后,指出子空间的可分性是同时可逼近性等价的必要条件.
[Abstract]:In this paper, we study the best simultaneous approximation of Minkowski norm relative to Euclidean space in Bochner-Lebesgue space. Firstly, the best simultaneous approximation represented by the distance function is described. Then, by using the measurable selection theorem, it is proved that its function is valued in the Bochner-Lebesgue space of a closed molecular space, and its simultaneous approximation is equivalent to the simultaneous approximation of the closed molecular space. Finally, it is pointed out that the separability of subspaces is a necessary condition for simultaneous approximation equivalence.
【作者单位】： 海南师范大学数学与统计学院;
【基金】：The National Natural Science Foundation of China(11361020)
【分类号】：O174.41
本文编号：2333388
[Abstract]:In this paper, we study the best simultaneous approximation of Minkowski norm relative to Euclidean space in Bochner-Lebesgue space. Firstly, the best simultaneous approximation represented by the distance function is described. Then, by using the measurable selection theorem, it is proved that its function is valued in the Bochner-Lebesgue space of a closed molecular space, and its simultaneous approximation is equivalent to the simultaneous approximation of the closed molecular space. Finally, it is pointed out that the separability of subspaces is a necessary condition for simultaneous approximation equivalence.
【作者单位】： 海南师范大学数学与统计学院;
【基金】：The National Natural Science Foundation of China(11361020)
【分类号】：O174.41
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