@article{8995ffd4c1a84b0f96027db3b9106841,
title = "Schoenberg coefficients and curvature at the origin of continuous isotropic positive definite kernels on spheres",
abstract = "We consider the class Ψd of continuous functions that define isotropic covariance functions in the d-dimensional sphere Sd. We provide a new recurrence formula for the solution of Problem 1 in Gneiting (2013b), solved by Fiedler (2013). In addition, we have improved the current bounds for the curvature at the origin of locally supported covariances (Problem 3 in Gneiting (2013b)), which is of applied interest at least for d=2.",
keywords = "Gegenbauer polynomials, Isotropic covariance function, Positive definite kernel, Schoenberg coefficients",
author = "Ahmed Arafat and Pablo Gregori and Emilio Porcu",
note = "Funding Information: Ahmed Arafat and Pablo Gregori{\textquoteright}s research are supported by Spanish Ministerio de Econom{\'i}a, Industria y Competitividad ([project MTM2016-78917-R ]) and Universitat Jaume I de Castell{\'o}n, Spain ([project P1.1B2015-40 ]). Emilio Porcu is supported by Chilean Proyecto Fondecyt, Chile [number 1170290 ]. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",
year = "2020",
month = jan,
doi = "10.1016/j.spl.2019.108618",
language = "British English",
volume = "156",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier B.V.",
}