Decay of Singular Values of Power Series Kernels on the Sphere

ABSTRACT

In this article, we provide decay rates for singular values of compact integral operators generated by power series kernels on either the unit sphere or the closed unit ball in ℝ^m + 1, m ≥ 1 under decay assumptions on the coefficients in the expansion of the kernel. The results are illustrated in concrete examples, including an integral operator generated by a Gaussian kernel on the sphere.

KEYWORDS:

• Compact integral operators
• decay rates
• Gaussian kernel
• power series kernels
• singular values
• sphere
• unit ball

MATHEMATICS SUBJECT CLASSIFICATION:

• 45C05
• 45P05
• 47A75
• 47B34
• 47B38
• 47G10