Covering number of the unit ball of Reproducing Kernel Hilbert Space of Schoenbergs kernels

• Ano de defesa: 2023
• Autor(a) principal: Gonzalez, Karina Navarro
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Covering numbers; Espaços de Hilbert de reprodução; Harmônicos esféricos; Kernel de Schoenberg; Números de cobertura; Reproducing kernel Hilbert space; Schoenbergs kernel; Spherical harmonics
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-08012024-114709/

In this work, we present accurate upper and lower bounds for the entropy/covering numbers of the unit ball for two general classes of Reproducing Kernel Hilbert Space (RKHS) on the unit sphere of Rd+1. In both classes, the RKHS is generated by an Schoenberg type kernel, it means, a positive definite continuous and zonal kernel. The upper and lower bounds we present carry precise information about the asymptotic constants, depending on the dimension of the sphere and the monotonic behavior of the Schoenberg/Fourier coefficients of the kernel we work with.