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An Introduction to the Theory of Reproducing Kernel Hilbert Spaces


Part of Cambridge Studies in Advanced Mathematics

  • Date Published: April 2016
  • availability: Available
  • format: Hardback
  • isbn: 9781107104099

£ 60.99

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About the Authors
  • 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.

    • 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
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    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

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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.

  • Authors

    Vern I. Paulsen, University of Waterloo, Ontario
    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, United Services Automobile Association
    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.

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