Recurrence relations for radial positive definite functions |
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| Authors: | Wolfgang zu Castell |
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| Institution: | Institute of Biomathematics and Biometry, GSF-National Research Center for Environment and Health, Ingolstaedter Landstrasse 1, 85764 Neuherberg, Germany |
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| Abstract: | In the theory of radial basis functions as well as in the theory of spherically symmetric characteristic functions recurrence relations are used to construct d-dimensional functions starting with lower-dimensional ones. We show that the operators used so far are special cases of one step recurrence relations for ?2-radial positive definite functions. We further give the analogue for ?1-radial functions and thereby define a turning bands operator for 1-symmetric characteristic functions. |
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| Keywords: | Radial basis functions Spherically symmetric characteristic functions Turning bands operator Fractional operators Meijer's G-function |
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