Strictly positive definite non-isotropic kernels on two-point homogeneous manifolds: The asymptotic approach

2022/05/15 by Jean Carlo Guella, Guella, Jean Carlo, Janin Jäger +1
Computer Science · Mathematics · Engineering · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2205.07396

Abstract

We present sufficient condition for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their representation as a series of spherical harmonics. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details.

Related

• Strictly positive definite kernels on two-point compact homogeneous spaces
• Strict positive definiteness on a product of compact two-point homogeneous spaces
• Strictly positive definite kernels on compact Riemannian manifolds
• Strict positive definiteness of convolutional and axially symmetric kernels on d-dimensional spheres
• Positive definite singular kernels on two-point homogeneous spaces