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  3. An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
  • Cited by 183
Publisher:
Cambridge University Press
Online publication date:
April 2016
Print publication year:
2016
Online ISBN:
9781316219232
DOI:
https://doi.org/10.1017/CBO9781316219232
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Cambridge Studies in Advanced Mathematics (152)
Information

Book description

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.

Reviews

'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 Source: Zentralblatt MATH

‘Anyone looking for a nice introduction to this theory need look no further.’

Jeff Ibbotson Source: MAA Reviews

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Contents

Contents
References
Bibliography
[1] Jim, Agler and John E., McCarthy, Pick interpolation and Hilbert function spaces, Graduate Studies in Mathematics, vol. 44, American Mathematical Society, Providence, Rhode Island, 2002.
[2] N., Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404. MR0051437 (14,479c)
[3] R. F., Bass, Stochastic processes, Cambridge Series in Statistical and Probabilistic Mathematics, vol. 33, Cambridge University Press, Cambridge, UK, 2011.
[4] S., Bergman, Ueber die Entwicklung der harmonischen Funktionen der Ebene und des Raumes nach Orthogonalfunktionen, Math. Ann. 86, (1922).
[5] Louis de, Branges and James, Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York, 1966. MR0215065 (35 #5909)
[6] Louis de, Branges, Hilbert spaces of entire functions, Prentice-Hall Inc., Englewood Cliffs, N.J., 1968. MR0229011 (37 #4590)
[7] John B., Conway, A course in functional analysis, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990. MR1070713 (91e:46001)
[8] Ronald G., Douglas and Vern I., Paulsen, Hilbert modules over function algebras, Pitman Research Notes in Mathematics, vol. 217, Longman Scientific, 1989.
[9] Gerald B., Folland, Real analysis: modern techniques and their applications, John Wiley & Sons, Inc., New York, 1999.
[10] E. H., Moore, General analysis. 2, Vol. 1, 1939.
[11] Sheldon, Ross, A first course in probability, 9th ed., Pearson Education Limited, Harlow, Esex, England, 2012.
[12] Donald, Sarason, Complex function theory, American Mathematical Society, Providence, Rhode Island, 2007.
[13] Elias M., Stein and Rami, Shakarchi, Real analysis: measure theory, integration, and Hilbert spaces, Princeton Lectures in Analysis III, Princeton University Press, Princeton, New Jersey, 2005.
[14] Christopher K. I., Williams and Carl Edward, Rasmussen, Gaussian processes for machine learning, MIT Press, 2006.

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