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Conditionally Positive Definite Matrix Valued Kernels on Euclidean Spaces

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Abstract

The purpose of this paper is to provide necessary and sufficient conditions on a continuous and matrix valued radial kernel on a Euclidean space in order that it be conditionally positive definite of a fixed order. Except for the one dimensional Euclidean space, the strict conditional positive definiteness of the kernel is fully characterized.

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Acknowledgements

The first author acknowledges partial support by CNPq, under grant 154360/2016-3. The second author acknowledges partial support by FAPESP, grant 2016/09906-0.

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  1. Departamento de Matemática, ICMC-USP, Caixa Postal 668, São Carlos, SP, 13560-970, Brazil

    J. C. Guella & V. A. Menegatto

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  1. J. C. Guella
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  2. V. A. Menegatto
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Correspondence to J. C. Guella.

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Communicated by Allan Pinkus.

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Guella, J.C., Menegatto, V.A. Conditionally Positive Definite Matrix Valued Kernels on Euclidean Spaces. Constr Approx 52, 65–92 (2020). https://doi.org/10.1007/s00365-019-09478-x

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