Isotropic Positive Definite Functions on Spheres

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

1 Scopus Citations
View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Article number109287
Journal / PublicationJournal of Functional Analysis
Volume282
Issue number1
Online published19 Oct 2021
Publication statusPublished - 1 Jan 2022

Abstract

In this paper, we investigate the relationship between positive definite functions on the unit sphere Sd and on the Euclidean space Rd. For the dimension d to be odd, a new technique is developed to establish the inheritance of positive (semi-)definite property from Rto Sand the converse. For d = 2, it is proved that a function defined by fθ,δ(t) = (θt)δ+, δd + 1/2 is positive definite on the unit sphere Sby restricting θ in an absolute range. Our results can verify a conjecture proposed by R.K. Beatson, W. zu Castell, Y. Xu and a sharp Pólya type criterion for positive definite functions on spheres.

Research Area(s)

  • Positive definite functions, Sphere, Positive integrals, Jacobi polynomials

Bibliographic Note

Research Unit(s) information for this publication is provided by the author(s) concerned.

Citation Format(s)

Isotropic Positive Definite Functions on Spheres. / Feng, Han; Ge, Yan.
In: Journal of Functional Analysis, Vol. 282, No. 1, 109287, 01.01.2022.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review