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Sharp estimates for the covering numbers of the Weierstrass fractal kernel |
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| Institution: | 1. DAMAT-UTFPR, Av. Alberto Carazzai, 1640, 863000-000, Cornelio Procopio, Brazil;2. ICMC, Universidade de São Paulo, Brazil;3. ICMC, Universidade de São Paulo, Av. Trabalhador saocarlense, 400, São Carlos, São Paulo, 13566-590, Brazil |
| Abstract: | In this paper, we present sharp estimates for the covering numbers of the embedding of the reproducing kernel Hilbert space (RKHS) associated with the Weierstrass fractal kernel into the space of continuous functions. The method we apply is based on the characterization of the infinite-dimensional RKHS generated by the Weierstrass fractal kernel and it requires estimates for the norm operator of orthogonal projections on the RKHS. |
| Keywords: | Covering numbers Weierstrass fractal kernel Fourier series Reproducing kernel Hilbert space |
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