Abstract
The goals of this chapter are to: Formally introduce positive and negative definite kernels, Describe the properties of positive and negative definite kernels, Provide examples of positive and negative definite kernels and to characterize coarse embeddings in a Hilbert space, Introduce strictly and strongly positive and negative definite kernels.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aronszajn N (1950) Theory of reproducing kernels. Trans Am Math Soc 68:337–404
Bochner S (1933) Integration von funktionen, deren werte die elemente eines vektorraumes sind. Fund Math 20:262–276
Kolmogorov AN (1941) Stationary sequences in Hilbert space. Bull MGU (in Russian) 2:1–40
Krein MG (1940) On the problem of prolongation of Hermitian positive functions. Dokl Akad Nauk (in Russian) 26:17–22
Schoenberg IJ (1938) Metric spaces and positive definite functions. Trans Am Math Soc 44(3):552–563
Vakhaniya NN, Tarieladze VI, Chobanyan SA (1985) Probability distributions in Banach spaces. Nauka, Moscow (in Russian)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Rachev, S.T., Klebanov, L.B., Stoyanov, S.V., Fabozzi, F.J. (2013). Positive and Negative Definite Kernels and Their Properties. In: The Methods of Distances in the Theory of Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4869-3_21
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4869-3_21
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4868-6
Online ISBN: 978-1-4614-4869-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)