Premium
Covering numbers of isotropic reproducing kernels on compact two‐point homogeneous spaces
Author(s) -
Azevedo Douglas,
Barbosa Victor S.
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600125
Subject(s) - mathematics , isotropy , unit sphere , kernel (algebra) , reproducing kernel hilbert space , homogeneous , mathematical analysis , fourier series , hilbert space , ball (mathematics) , series (stratigraphy) , pure mathematics , combinatorics , paleontology , physics , quantum mechanics , biology
In this paper we present upper and lower estimates for the covering numbers of the unit ball of a reproducing kernel Hilbert space associated to a continuous isotropic kernel on a compact two‐point homogeneous space (CTPHS). These estimates are obtained from estimates on the decay of the Fourier–Jacobi coefficients of the kernel via applications of the Funk–Hecke formula and the Schoenberg series representation of an isotropic kernel on CTPHS and also by the use of cubature formulas on these spaces.