Journal article

Publication year: 2019

Journal: Symmetry, Integrability and Geometry: Methods and Applications

Volume number: 15

ISSN: 1815-0659

Open access status: Gold

DOI Link: https://doi.org/10.3842/SIGMA.2019.081

Publisher: National Academy of Science of Ukraine

Abstract: 
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 Trubner and Ziegel, which says that for a positive definite function on the Hilbert sphere to be in C-2l ([0, pi]), it is necessary and sufficient for its infinity-Schoenberg sequence to satisfy Sigma(infinity)(m=0) a(m)m(l) < infinity.

Harvard Citation style: Jaeger, J. (2019) A Note on the Derivatives of Isotropic Positive Definite Functions on the Hilbert Sphere, Symmetry, Integrability and Geometry: Methods and Applications, 15, Article 081. https://doi.org/10.3842/SIGMA.2019.081

APA Citation style: Jaeger, J. (2019). A Note on the Derivatives of Isotropic Positive Definite Functions on the Hilbert Sphere. Symmetry, Integrability and Geometry: Methods and Applications. 15, Article 081. https://doi.org/10.3842/SIGMA.2019.081