Sharp estimates for the covering numbers of the Weierstrass fractal kernel
Functional Analysis
2021-10-12 v1
Abstract
In this paper, we use the infamous continuous and nowhere differentiable Weierstrass function as a prototype to define a Weierstrass fractal kernel. We investigate the properties of the reproducing kernel Hilbert space (RKHS) associated with this kernel by presenting an explicit characterization of this space. In particular, we show that this space has a dense subset composed of continuous but nowhere differentiable functions. Moreover, we present sharp estimates for the covering numbers of the unit ball of this space as a subset of the continuous functions.
Keywords
Cite
@article{arxiv.2110.04609,
title = {Sharp estimates for the covering numbers of the Weierstrass fractal kernel},
author = {Douglas Azevedo and Karina Gonzalez and Thais Jordão},
journal= {arXiv preprint arXiv:2110.04609},
year = {2021}
}
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16 pages