Reproducing Kernel (Quasi-)Banach Spaces with the $\ell^p$ Coefficient Norms

arXiv:2611.08032v1 Announce Type: new Abstract: This paper advances the theory of reproducing kernel Banach spaces (RKBSs) by investigating the general $\ell^p$ regularization framework, with a particular focus on the non-convex regime $0 1$, we construct RKBSs using a fixed countable dictionary, establish minimizer existence, and identify the optimal relaxed representer factor through an off-sample coefficient operator. These results reveal fundamental differences between the regimes $0 1$. Numerical experiments compare the accuracy and sparsity of solutions for these three cases.