Vern I. Paulsen

Introduction to the Theory of Reproducing Kernel Hilbert Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 11. April 2016
• Englisch
• ISBN-13: 9781316560297
• Artikelnr.: 44877728

Autorenporträt

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.

Inhaltsangabe

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.