On approximation tools and its applications on compact homogeneous spaces
Autor: | Carrijo, A. O., Jordão, T. |
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Rok vydání: | 2017 |
Předmět: | |
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 |
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