再生核Banach空间核的乘积性质  

Product properties of kernels in reproducing kernel Banach spaces

作　　者：孙靖 许安见 SUN Jing;XU Anjian(College of Science,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《内江师范学院学报》2024年第6期35-38,共4页Journal of Neijiang Normal University

基　　金：国家自然科学基金面上项目(11871127);重庆市自然科学基金项目(cstc2019jcyj-msxmX0295);重庆市教委科学技术研究项目(KJZD-K202301109)。

摘　　要：为了解决机器学习中最小范数插值、正则化网络、支持向量机、核主成分分析等问题,再生核Hilbert空间已经不能满足需要,于是Zhang等引入了再生核Banach空间.本文利用张量积及半内积的方法,证明了两个半内积再生核Banach空间的张量积也为对应再生核乘积所诱导的半内积再生核Banach空间.In order to solve the problems of minimum norm interpolation,regularized networks,support vector machines,and kernel principal component analysis in machine learning,reproducing kernel Hilbert space is no longer sufficient.Zhang et al.introduced the reproducing kernel Banach space.Using the method of tensor product and semi-inner product,it is proved that the tensor product of two semi-inner-product reproducing kernel Banach space is also the semi-inner-product reproducing kernel Banach space induced by the product of the corresponding reproducing kernels.

关 键 词：再生核HILBERT空间 再生核Banach空间 半内积 

分 类 号：O177.2[理学—数学]