An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
Part of Cambridge Studies in Advanced Mathematics
- Authors:
- Vern I. Paulsen, University of Waterloo, Ontario
- Mrinal Raghupathi, United Services Automobile Association
- Date Published: April 2016
- availability: Available
- format: Hardback
- isbn: 9781107104099
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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.
Read more- Provides a unified account of the topic, covering fundamental theory as well as applications
- Written at an accessible level suitable for a broad audience including graduate students and researchers
- Includes a wealth of detailed examples and end-of-chapter exercises
Reviews & endorsements
'The purpose of this fine monograph is two-fold. On the one hand, the authors introduce a wide audience to the basic theory of reproducing kernel Hilbert spaces (RKHS), on the other hand they present applications of this theory in a variety of areas of mathematics … the authors have succeeded in arranging a very readable modern presentation of RKHS and in conveying the relevance of this beautiful theory by many examples and applications.' Dirk Werner, Zentralblatt MATH
See more reviews'Anyone looking for a nice introduction to this theory need look no further.' Jeff Ibbotson, MAA Reviews
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×Product details
- Date Published: April 2016
- format: Hardback
- isbn: 9781107104099
- length: 192 pages
- dimensions: 235 x 156 x 15 mm
- weight: 0.39kg
- contains: 99 exercises
- availability: Available
Table of Contents
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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