An introduction to the theory of reproducing kernel Hilbert spaces
著者
書誌事項
An introduction to the theory of reproducing kernel Hilbert spaces
（Cambridge studies in advanced mathematics, 152）
Cambridge University Press, 2016
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注記
Bibliography: p. 180
Includes index
内容説明・目次
内容説明
Reproducing kernel Hilbert spaces have developed into an important tool in many areas, especially statistics and machine learning, and they play a valuable role in complex analysis, probability, group representation theory, and the theory of integral operators. This unique text offers a unified overview of the topic, providing detailed examples of applications, as well as covering the fundamental underlying theory, including chapters on interpolation and approximation, Cholesky and Schur operations on kernels, and vector-valued spaces. Self-contained and accessibly written, with exercises at the end of each chapter, this unrivalled treatment of the topic serves as an ideal introduction for graduate students across mathematics, computer science, and engineering, as well as a useful reference for researchers working in functional analysis or its applications.
目次
- Part I. General Theory: 1. Introduction
- 2. Fundamental results
- 3. Interpolation and approximation
- 4. Cholesky and Schur
- 5. Operations on kernels
- 6. Vector-valued spaces
- Part II. Applications and Examples: 7. Power series on balls and pull-backs
- 8. Statistics and machine learning
- 9. Negative definite functions
- 10. Positive definite functions on groups
- 11. Applications of RKHS to integral operators
- 12. Stochastic processes.
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