Strict positive definiteness on products of compact two-point homogeneous spaces

ABSTRACT

We present an explicit characterization for the real, continuous, isotropic and strictly positive definite kernels on a product of compact two-point homogeneous spaces, covering almost all possible choices for the spaces. The result complements similar characterizations previously obtained for products of high-dimensional spheres.

KEYWORDS:

• Two-point homogeneous spaces
• Jacobi polynomials
• Gauss hypergeometric function
• strict positive definiteness
• isotropy
• antipodal sets

AMS SUBJECT CLASSIFICATION:

• 22F30
• 33C05
• 33C45
• 33C55
• 42C10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was partially supported by CNPq, under grant [141908/2015-7]. The second one by FAPESP, under grant [2014/00277-5].