非紧区域上算子值再生核的Mercer定理

Mercer Theorem for Operator-valued Reproducing Kernel on Noncompact Domain

多任务学习已经成为机器学习领域一个热门的课题.算子值再生核理论是多任务学习的重要数学基础.本文的主要工作是建立了非紧区域上算子值再生核的Mercer定理,从而将传统的紧区域上的再生核Hilbert空间理论推广到非紧区域上.

It is widely known that the multi-task learning has been a hot topic in machine learning. The operator-valued reproducing kernel and vector-valued reproducing kernel Hilbert space are the main mathematical foundations for multi-task learning. The main purpose of this paper is to establish a Mercer theorem for the operator-valued reproducing kernel on noncompact domain with σ-finite measure. Our result would provide valuable reference in this direction.