Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative

For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a similar characterization for kernels on the space-time setting G×S...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2018
Hauptverfasser: Bonfim, R.N., Guella, J.C., Menegatto, V.A.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2018
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/209845
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative / R.N. Bonfim, J.C. Guella, V.A. Menegatto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 29 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Beschreibung
Zusammenfassung:For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a similar characterization for kernels on the space-time setting G×Sᵈ, where G is a locally compact group, and Sᵈ is the unit sphere in ℝᵈ⁺¹, keeping isotropy of the kernels with respect to the Sᵈ component. Among other things, these results provide new procedures for the construction of valid models for interpolation and approximation on compact two-point homogeneous spaces.
ISSN:1815-0659