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Introduction to the theory of reproducing kernel Hilbert spaces / Vern I. Paulsen and Mrinal Raghupathi.

By: Contributor(s): Material type: TextTextSeries: Cambridge studies in advanced mathematics ; 152Publication details: Cambridge : Cambridge University Press, 2016.Description: x, 182 pages ; 24 cmISBN:
  • 9781107104099
Subject(s): DDC classification:
  • 515.733 23 P332
Contents:
Part 1 General theory: 1. Introduction -- 2. Fundamental results -- 3. Interpolation and approximation -- 4. Cholesky and Schur -- 5. Operations on kernals -- 6. Vector-valued spaces -- Part 2 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.
Summary: 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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Includes bibliographical references and index.

Part 1 General theory:
1. Introduction --
2. Fundamental results --
3. Interpolation and approximation --
4. Cholesky and Schur --
5. Operations on kernals --
6. Vector-valued spaces --
Part 2 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.

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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