Conditionally Positive Definite Functions and Their Application to Multivariate Interpolations
نویسندگان
چکیده
منابع مشابه
Multivariate positive definite functions on spheres
In 1942 I.J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a positive linear combination of the Gegenbauer polynomials. In this paper we extend Schoenberg’s theorem for multivariate Gegenbauer polynomials. This extension derives new positive semidefinite constraints for the distance distribution which can be applied for spherical codes.
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Since Aronszajn (1950), it is well known that a functional Hilbert space, called Reproducing Kernel Hilbert Space (R.K.H.S ), can be associated to any positive definite kernel K. This correspondance is the basis of many useful algorithms. In the more general context of conditionally positive definite kernels the native spaces are the usual theoretical framework. However, the definition of condi...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1993
ISSN: 0021-9045
DOI: 10.1006/jath.1993.1059