An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
Mrinal Raghupathi, United Services Automobile Association
AUD$117.95
inc GSTReproducing 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.
- 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
'Anyone looking for a nice introduction to this theory need look no further.' Jeff Ibbotson, MAA Reviews
Product details
April 2016Adobe eBook Reader
9781316560297
0 pages
0kg
99 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
