On approximation tools and its applications on compact homogeneous spaces

Autor:	Carrijo, A. O., Jordão, T.
Rok vydání:	2017
Předmět:	Mathematics - Functional Analysis 41A60 41A10 41A36 45C05 47A75
Druh dokumentu:	Working Paper
Popis:	We prove a characterization for the Peetre type $K$-functional on $\mathbb{M}$, a compact two-point homogeneous space, in terms the rate of approximation of a family of multipliers operator defined to this purpose. This extends the well known results on the spherical setting. The characterization is employed to show that an abstract H\"{o}lder condition or finite order of differentiability condition imposed on kernels generating certain operators implies a sharp decay rates for their eigenvalues sequences. The latest is employed to obtain estimates for the Kolmogorov $n$-width of unit balls in Reproducing Kernel Hilbert Space (RKHS). Comment: 15 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1708.02576 Zobrazit plný text záznamu View this record from Arxiv