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

• Опубліковано в: Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2019
• ISSN: 1815-0659
• Автор: Jäger, J.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2019
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/210307
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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...