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Conditionally Positive Definite Matrix Valued Kernels on Euclidean Spaces

  • J. C. GuellaEmail author
  • V. A. Menegatto
Article

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.

Keywords

Matrix valued kernels Conditionally positive definite Strictly conditionally positive definite Radial functions 

Mathematics Subject Classification

42A82 43A35 47A56 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticaICMC-USPSão CarlosBrazil

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