Reproducing Properties of Holomorphic Kernels on Balls of ℂq. (10th September 2018)

• Record Type: Journal Article
• Authors: Oliveira, C. P.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 12(2018)
• Page Start: 1229
• Page End: 1247
• Publication Date: 2018-09-10
• Subjects: Asymptotic behavior -- bergman kernel -- holomorphic monomial -- integral operator -- reproducing kernel Hilbert space; 15A18 -- 32A10 -- 32A25 -- 32A36 -- 42A82 -- 45C05 -- 45P05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1472103
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this work, we investigate the class of integral operators whose generating kernels have expansion series in terms of fundamental monomials. We study the reproducing kernel Hilbert space associated with such kernels, specifically when defined on balls about the origin ofℂ q . Consequently, spectral properties, including the asymptotic behavior of the eigenvalues of these operators will be obtained. We also revisit our main results in the case in which the generating kernel is the Bergman kernel.