典型文献
On Reproducing Kernel Banach Spaces:Generic Definitions and Unified Framework of Constructions
文献摘要：
Recently,there has been emerging interest in constructing reproducing kernel Banach spaces(RKBS)for applied and theoretical purposes such as machine learning,sampling reconstruction,sparse approximation and functional analysis.Existing constructions include the reflexive RKBS via a bilinear form,the semi-inner-product RKBS,the RKBS with l1 norm,the p-norm RKBS via generalized Mercer kernels,etc.The definitions of RKBS and the associated reproducing kernel in those references are dependent on the construction.Moreover,relations among those constructions are unclear.We explore a generic definition of RKBS and the reproducing kernel for RKBS that is independent of construction.Furthermore,we propose a framework of constructing RKBSs that leads to new RKBSs based on Orlicz spaces and unifies existing constructions mentioned above via a continuous bilinear form and a pair of feature maps.Finally,we develop representer theorems for machine learning in RKBSs constructed in our framework,which also unifies representer theorems in existing RKBSs.
文献关键词：
中图分类号：
作者姓名：
Rong Rong LIN;Hai Zhang ZHANG;Jun ZHANG
作者机构：
School of Mathematics and Statistics,Guangdong University of Technology,Guangzhou 510520,P.R.China;School of Mathematics(Zhuhai),and Guangdong Province Key Laboratory of Computational Science,Sun Yat-sen University,Zhuhai 519082,P.R.China;Department of Psychology and Department of Statistics,University of Michigan,Ann Arbor,MI 48109,USA
文献出处：
引用格式：
[1]Rong Rong LIN;Hai Zhang ZHANG;Jun ZHANG-.On Reproducing Kernel Banach Spaces:Generic Definitions and Unified Framework of Constructions)[J].数学学报（英文版）,2022(08):1459-1483
A类：
RKBS,RKBSs,representer
B类：
On,Reproducing,Kernel,Banach,Spaces,Generic,Definitions,Unified,Framework,Constructions,Recently,there,has,been,emerging,interest,constructing,reproducing,spaces,applied,theoretical,purposes,such,machine,learning,sampling,reconstruction,sparse,approximation,functional,analysis,Existing,constructions,include,reflexive,via,bilinear,form,semi,inner,product,l1,norm,generalized,Mercer,kernels,etc,definitions,associated,those,references,are,Moreover,relations,among,unclear,We,explore,generic,that,independent,Furthermore,we,propose,framework,leads,new,Orlicz,unifies,existing,mentioned,above,continuous,pair,feature,maps,Finally,develop,theorems,constructed,our,which,also
AB值：
0.534026
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