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.
A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.
Vern I. Paulsen held a John and Rebecca Moores Chair in the Department of Mathematics, University of Houston, from 1996 to 2015. He is currently a Professor in the Department of Pure Mathematics at the Institute for Quantum Computing, University of Waterloo. He is the author of four books, over 100 research articles, and the winner of several teaching awards. Mrinal Raghupathi is a Lead Quantitative Risk Analyst at the United Services Automobile Association (USAA). His research involves applications of reproducing kernel Hilbert spaces, risk analysis, and model validation.
'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
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