论文信息 - Strictly positive definite kernels on the Hilbert sphere

Strictly positive definite kernels on the Hilbert sphere

We completely characterize the strictly positive definite and the strictly conditionally negative definite radial continuous kernels on the real Hilbert sphere. Any functions generating such kernels, can be used in radial basis interpolation of arbitrary data on a set of points in any finite–dimensional sphere.

Valdir A. Menegatto | V. A. Menegatto | V. Menegatto

[1] C. Berg,et al. Harmonic Analysis on Semigroups , 1984 .

[2] I. J. Schoenberg. Remarks to Maurice Frechet's Article ``Sur La Definition Axiomatique D'Une Classe D'Espace Distances Vectoriellement Applicable Sur L'Espace De Hilbert , 1935 .

[3] Yuan Xu,et al. Strictly positive definite functions on spheres , 1992 .

[4] N. Bingham. Positive definite functions on spheres , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.

[5] Charles R. Johnson,et al. Topics in Matrix Analysis , 1991 .

[6] Interpolation by periodic radial functions , 1992 .

[7] I. S. Gradshteyn,et al. Table of Integrals, Series, and Products , 1976 .

[8] D. V. Widder,et al. The Laplace Transform , 1943 .

[9] Nira Dyn,et al. Interpolation by piecewise-linear radial basis functions, II , 1989 .

[10] C. Micchelli. Interpolation of scattered data: Distance matrices and conditionally positive definite functions , 1986 .

[11] Yuan Xu,et al. A SET OF RESEARCH PROBLEMS IN APPROXIMATION THEORY , 1993 .

[12] I. J. Schoenberg. Positive definite functions on spheres , 1942 .

[13] G. Pólya,et al. Problems and theorems in analysis , 1983 .

[14] Will Light,et al. Interpolation by periodic radial basis functions , 1992 .