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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
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eBook
Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
2019
Overview
This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing
kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be
well-posed and of easy implementation. First we verify many advanced properties of the general RKBSs such as density, continuity,
separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and
universal approximation. Then, we develop a new concept of generalized Mercer kernels to construct
Publisher
American Mathematical Society
Subject
ISBN
9781470435509, 1470435500
