Isotropic Positive Definite Functions on Spheres
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Article number | 109287 |
| Journal / Publication | Journal of Functional Analysis |
| Volume | 282 |
| Issue number | 1 |
| Online published | 19 Oct 2021 |
| Publication status | Published - 1 Jan 2022 |
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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 Rd to Sd and the converse. For d = 2, it is proved that a function defined by fθ,δ(t) = (θ − t)δ+, δ ≥
d + 1/2 is positive definite on the unit sphere S2 by 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 journal › peer-review
