A Note on the Derivatives of Isotropic Positive Definite Functions on the Hilbert Sphere

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2019
• 1. Verfasser: Jäger, J.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2019
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/210307
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: A Note on the Derivatives of Isotropic Positive Definite Functions on the Hilbert Sphere / J. Jäger // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 23 назв. — англ.

In this note, we give a recursive formula for the derivatives of isotropic positive definite functions on the Hilbert sphere. We then use it to prove a conjecture stated by Trübner and Ziegel, which says that for a positive definite function on the Hilbert sphere to be in C²ˡ([0,π]), it is necessary...