A Fock space approach to the theory of kernel functions

A Fock space approach to the theory of kernel functions

In this paper, we give a new approach to the theory of kernel functions. Our method is based on the structure of Fock spaces. As its applications, two non-Euclidean examples of strictly positive kernel functions are given. Moreover, we give a new proof of the universal approximation theorem for Gaus...

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2024-02, Vol.28 (1), p.9, Article 9
1. Verfasser: Seto, Michio
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Approximation
Calculus of Variations and Optimal Control
Optimization
Construction
Econometrics
Fourier Analysis
Hilbert space
Kernel functions
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
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Zusammenfassung:In this paper, we give a new approach to the theory of kernel functions. Our method is based on the structure of Fock spaces. As its applications, two non-Euclidean examples of strictly positive kernel functions are given. Moreover, we give a new proof of the universal approximation theorem for Gaussian type kernels.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-023-01028-x