Generalized Mercer Keels and Reproducing Keel Banach Spaces (Memoirs of the American Mathematical Society)

by: Yuesheng Xu (Author),Qi Ye(Author)

Publisher: Amer Mathematical Society

Publication Date: 2019/4/1

Language: English

Print Length: 122 pages

ISBN-10: 1470435500

ISBN-13: 9781470435509

Book Description

This article studies constructions of reproducing keel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing keel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing keels such that machine leaing in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for leaing methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer keels to construct $p$-norm RKBSs for $1leq pleqinfty$.

About the Author

This article studies constructions of reproducing keel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing keel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing keels such that machine leaing in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for leaing methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer keels to construct $p$-norm RKBSs for $1leq pleqinfty$.

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