Decay of Singular Values of Power Series Kernels on the Sphere. (2nd April 2016)

• Record Type: Journal Article
• Authors: Azevedo, D.; Menegatto, V. A.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 4(2016)
• Page Start: 440
• Page End: 458
• Publication Date: 2016-04-02
• Subjects: Compact integral operators -- decay rates -- Gaussian kernel -- power series kernels -- singular values -- sphere -- unit ball; 45C05 -- 45P05 -- 47A75 -- 47B34 -- 47B38 -- 47G10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1136890
• Languages: English
• ISSNs: 0163-0563

Abstract

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.