Conditionally Positive Definite Matrix Valued Kernels on Euclidean Spaces

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


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.


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

Mathematics Subject Classification

42A82 43A35 47A56 



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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Authors and Affiliations

  1. 1.Departamento de MatemáticaICMC-USPSão CarlosBrazil

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