Conditionally Positive Definite Matrix Valued Kernels on Euclidean Spaces

Conditionally Positive Definite Matrix Valued Kernels on Euclidean Spaces

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 defin...

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Veröffentlicht in:Constructive approximation 2020-08, Vol.52 (1), p.65-92
Hauptverfasser: Guella, J. C., Menegatto, V. A.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Euclidean geometry
Euclidean space
Kernels
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrix methods
Numerical Analysis
Physical Sciences
Science & Technology
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Beschreibung
Zusammenfassung: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.
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-019-09478-x