An Introduction to the Theory of Reproducing Kernel Hilbert Spaces

Covering the fundamental underlying theory as well as a range of applications, this unique text provides a unified overview of reproducing kernel Hilbert spaces. It offers an unrivalled and accessible introduction to the field, ideal for graduate students and researchers working in functional analysis or its applications.

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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.