An Introduction to the Theory of Reproducing Kernel Hilbert Spaces

ISBN-13: 9781107104099 / Angielski / Twarda / 2016 / 192 str.

Vern Paulsen; Mrinal Raghupathi

Opis

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.

Recenzje

'Anyone looking for a nice introduction to this theory need look no further.' Jeff Ibbotson, MAA Reviews

Spis treści

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.