%0 Journal Article
%T Reproducing Kernel Banach Spaces with the l1 Norm
%A Guohui Song
%A Haizhang Zhang
%A Fred J. Hickernell
%J Computer Science
%D 2011
%I arXiv
%R 10.1016/j.acha.2012.03.009
%X Targeting at sparse learning, we construct Banach spaces B of functions on an input space X with the properties that (1) B possesses an l1 norm in the sense that it is isometrically isomorphic to the Banach space of integrable functions on X with respect to the counting measure; (2) point evaluations are continuous linear functionals on B and are representable through a bilinear form with a kernel function; (3) regularized learning schemes on B satisfy the linear representer theorem. Examples of kernel functions admissible for the construction of such spaces are given.
%U http://arxiv.org/abs/1101.4388v3