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arXiv · 1708.02576

On approximation tools and its applications on compact homogeneous spaces

A. O. Carrijo·T. Jordão
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Abstract

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).

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A. O. Carrijo, T. Jordão. 2017-08-08. On approximation tools and its applications on compact homogeneous spaces. https://arxiv.org/abs/1708.02576

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