Reproducing Kernel Banach Spaces with the l1 Norm

Guohui Song; Haizhang Zhang; Fred J. Hickernell

doi:10.1016/j.acha.2012.03.009

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arXiv · 1101.4388

Reproducing Kernel Banach Spaces with the l1 Norm

Guohui Song·Haizhang Zhang·Fred J. Hickernell

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Abstract

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.

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Guohui Song, Haizhang Zhang, Fred J. Hickernell. 2012-03-28. Reproducing Kernel Banach Spaces with the l1 Norm. https://doi.org/10.1016/j.acha.2012.03.009

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