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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Yuesheng Xu Syracuse University, Syracuse, NY
Qi Ye South China Normal University, Guangzhou, China
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Softcover ISBN: 978-1-4704-3550-9
Product Code: MEMO/258/1243
List Price: $81.00 MAA Member Price:$72.90
AMS Member Price: $48.60 Electronic ISBN: 978-1-4704-5077-9 Product Code: MEMO/258/1243.E List Price:$81.00
MAA Member Price: $72.90 AMS Member Price:$48.60
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List Price: $121.50 MAA Member Price:$109.35
AMS Member Price: $72.90 Click above image for expanded view Generalized Mercer Kernels and Reproducing Kernel Banach Spaces Yuesheng Xu Syracuse University, Syracuse, NY Qi Ye South China Normal University, Guangzhou, China Available Formats:  Softcover ISBN: 978-1-4704-3550-9 Product Code: MEMO/258/1243  List Price:$81.00 MAA Member Price: $72.90 AMS Member Price:$48.60
 Electronic ISBN: 978-1-4704-5077-9 Product Code: MEMO/258/1243.E
 List Price: $81.00 MAA Member Price:$72.90 AMS Member Price: $48.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$121.50 MAA Member Price: $109.35 AMS Member Price:$72.90
• Book Details

Memoirs of the American Mathematical Society
Volume: 2582019; 122 pp
MSC: Primary 68; 94; Secondary 46;

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 the authors 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, they develop a new concept of generalized Mercer kernels to construct $p$-norm RKBSs for $1\leq p\leq\infty$.

• Chapters
• 1. Introduction
• 2. Reproducing Kernel Banach Spaces
• 3. Generalized Mercer Kernels
• 4. Positive Definite Kernels
• 5. Support Vector Machines
• 6. Concluding Remarks
• Acknowledgments

• Requests

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Volume: 2582019; 122 pp
MSC: Primary 68; 94; Secondary 46;

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 the authors 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, they develop a new concept of generalized Mercer kernels to construct $p$-norm RKBSs for $1\leq p\leq\infty$.

• Chapters
• 1. Introduction
• 2. Reproducing Kernel Banach Spaces
• 3. Generalized Mercer Kernels
• 4. Positive Definite Kernels
• 5. Support Vector Machines
• 6. Concluding Remarks
• Acknowledgments
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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